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It is the 'sine' ratio for a right angle triangle
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How do you find the remaining legs of a 45 45 90 isosceles right triangle given a hypotenuse of 48 inches?
trig functions sin(45o) = opposite/hypotenuse sin(45o) = opp/48 inches 48 inches * sin(45o) = opposite = 34 inches ===============you do other side with appropriate trig function Update: Use Pythagoras. Adj^2 + Opp^2 = Hyp^2 (For Isosceles right angles triangle Adj = Opp) Therefore, Adj = Opp = Sqrt((Hyp^2)/2) = 33.9
How do you find the height of an equilateral triangle if you have the length of the hypotenuse?
An equilateral triangle hasn't a hypotenuse; hypotenuse means the side opposite the right angle in a right triangle. An equilateral triangle has no right angles; rather all three of its angles measure 60 degrees. Knowing the length of the hypotenuse of a right triangle does not give enough information to determine the triangle's height. But the length of a side (which is the same for every side) of an equilateral triangle is enough information from which to calculate the height of that triangle. The first way is simply to use the formula that has been developed for this purpose: height = (length X sqrt(3)) / 2. But you can also use the geometry of right triangles to solve for the height. That is because you can bisect the triangle with a vertical line from the top vertex to the center of the base. The length of that line, which splits the equilateral triangle into two right triangles, is the height of the equilateral triangle. We know a lot about each right triangle formed by bisecting the equilateral triangle: * - The hypotenuse length is the length of the equilateral triangle's side. * - The base length is half the length of the hypotenuse. * - The angle opposite the hypotenuse is 90 degrees. * - The angle opposite the vertical is 60 degrees (the measure of every angle of any equilateral triangle). * - The angle opposite the base is 30 degrees (half of the bisected 60-degree angle). * - (Note that the sum of the angles does equal 180 degrees, as it must.) Now to solve for the height of a right triangle. There are a few ways. For labeling, let's let h=height of the equilateral triangle and the vertical side of the right triangle; A=every angle of the equilateral triangle (each 60o); s=side length of any side of the equilateral triangle and thus the hypotenuse of the right triangle. Since the sine of an angle of a right triangle is equal to the ratio of the opposite side divided by the hypotenuse, we can write that sin(A) = h/s. Solving for h, we get h=sin(A)/s. With trig tables you can now easily find the height.
How do you find the angle measurements of a triangle if you have the side lengths?
The way to find the angle measures of a triangle if you have the side lengths is to use inverse trigonometry. If a triangle is a right triangle (meaning it has one right angle or 90 degree angle) then you can use Right Triangle Trigonometry. There are three trigonometric (or trig) functions that we can use: Sin (pronounced Sign, short for sine), Cos (short for cosine), and Tan (short for tangent). These are all names of functions. These functions relate an angle measure of a right triangle to the ratio of two particular sides. Generally SOH CAH TOA is the mnemonic device people use to remember the trig ratios. Sin(x) = Opposite/Hypotenuse Cos(x) = Adjacent/Hypotenuse Tan(x) = Opposite/Adjacent. In each of these relationships, x is the value of one of the acute angles of the triangle. We want to however, find the angle measure rather than the ratio of the sides. So to do this, we isolate the value of the angle by taking the inverse function of both sides, resulting in the following equations where x is the value of the acute angle: x = sin-1(opposite/hypotenuse) or x = cos-1(adjacent/hypotenuse) or x = tan-1(opposite/adjacent). The negative one that you see here is just denoting that you need to use the inverse of the function. Most calculators that have the trig functions available, also have the inverses available as well. As a quick example, take the following right triangle ABC: A |\ |.\ |..\ |...\ |....\ |.....\ C----B If AB=5, BC=3, and AC=4 and we know that C is a right angle, we can find angle B by doing the following calculation on the calculator: the measure of angle B=tan-1(4/3) The calculator would yield an answer of roughly 53.1 degrees. If the triangle is not a right triangle, then you either have to use the law of cosine or the law of sin, both of which are very well explained on wikipedia. They are simply ways to relate side lengths to angle measures using the trig functions.
How is sin 90 equal to 1?
Buckle up, 'cause we can't draw diagrams here and we have to explain everything. Let's jump. Draw a graph with an x-axis and a y-axis like usual. Don't use graph paper or a ruler unless you have to. Just eyeball the thing. We're going to draw a right triangle on the graph and here's how we'll do it. Start at the origin, (0, 0) and draw a line along the x-axis about "6 or 7 units" long. Now draw a line from the end of the first one straight up (at a right angle to the x-axis) and make it about "2 units" long. Lastly, draw the "slanted" line from the origin up to where the vertical line ended. That last line was the hypotenuse of your nice right triangle. Got a good picture? Super. Let's jump to some review. The trigonometry (trig) function called the "sine" (sin) is the relationship in any right triangle between the length of the opposite side (to an given angle in the triangle) and the length of the hypotenuse of that triangle. It's actually the length of the opposite side of the triangle divided by the length of the hypotenuse of the triangle. This number is a "pure" number without units because the units (inches, feet, miles - whatever) cancel out when the division is made. Now that we've reviewed the sine function, let's take it to our triangle. Look at the angle made by the first line you drew and the last one you drew (which was the hypotenuse). It's the angle with the origin of the graph (0, 0) as the vertex. It's gonna be 25 to 35 degrees or so, ballpark. We don't need to be exact. Now, the sine of that angle is the length of the opposite side divided by the length of the hypotenuse. It's some number between 0 and 1. The hypotenuse is obviously larger, and we'll end up with a fraction or, if you prefer, a decimal number. We don't need to know what it is because we are going to be looking at a "trend" or "shift" as we change our graph. We have some number as the sine, and we're good. Now let's modify our graph and draw a new triangle. Follow closely when we jump. We are going to "keep" the hypotenuse we drew. But we are going to "rotate it up" to make a new triangle. Note that we won't change its length. We're going to "open up" the angle between the x-axis and the hypotenuse. Let's do that by detatching the hypotenuse from the short vertical to the x-axis (which is that little second line we drew). Swing the hypotenuse up (that's counterclockwise from its first position) and put it about "half way" between where it was and where the y-axis is. Got it located? Now "drop a perpendicular" from the end of the hypotenuse to the x-axis, and make the line perpendicular to the x-axis. This forms a new right triangle. And this new triangle has a longer "second side" that is vertical to the x-axis. Let's look at our new triangle. The "new" angle formed by the x-axis and the new location of the hypotenuse is larger than it was. And the sine for that angle has changed. The sine is (again) the length of the opposite side over the length of the hypotenuse, and notice that the "new" opposite side is longer than the old one. (We can call that side, the one perpenducular to the x-axis, the "second side" here.) That means the "new" sine will be a larger fraction or a larger decimal (if you work it that way) than before. We don't know the exact number, but we only need to look at it in comparison to what it was. And it's bigger. So let's rotate the hypotenuse more. Start moving it in a slow but continuous motion in the counterclockwise direction. It's heading for the y-axis as you rotate it. Now focus. The new triangle formed as we rotate the hypotenuse (again, without changing its length) will have a longer and longer "perpendicular" to the x-axis as we move the hypotenuse. Pretend that the second side, the one we keep making longer as we rotate the hypotenuse up, is a rubber band stretching longer and longer as we rotate the hypotenuse. It still has to make a right angle where it is attached to the x-axis, so it must "slide along" that axis toward the origin to keep the angle at 90 degrees. Make sense? The triangle is "getting taller" as we rotate the hypotenuse. And the base is getting shorter and shorter. Through all this, the sine of the angle we are looking at is getting bigger and bigger. See how it works? One more jump. As the hypotenuse is rotated counter clockwise and approaches the y-axis, the length of that "second side" will continue to grow and will actually approach the length of the hypotenuse itself. (The triangle's base gets tinier and tinier through all this.) Our angle is getting bigger and bigger, too, and it is approaching 90 degrees. As the length of the second side approaches the length of the hypotenuse, the sine of the angle, that is, the length of the second side divided by the length of the hypotenuse, actually approaches one. That's because the second side is getting almost as long as the hypotenuse. Closer and closer to vertical we move that hypotenuse. At vertical, that is, when the hypotenuse is rotated to vertical, the triangle "disappears" from view, but imagine what is happeing as we approach this "vanishing point" where the triangle ceases to exist. At 90 degrees, the second side is the exact same length as the hypotenuse. That means the angle formed at the vertex becomes 90 degrees. And the base will be so short as to disappear as well. At the 90 degree point where the hypotenuse has been rotated up to lie along the y-axis, the length of the opposite will equal to the length of the hypotenuse. And the sine of the angle (which is 90 degrees) will be the length of the second side exactly 1 at this point. The sine of an angle varies as the measure of the angle, and as the angle increases in measure from 0 to 90 degrees, the sine of the angle varies from 0 to 1 as we discovered.
What is a adjacent side?
Two things that are adjacent to each other are in contact with each other without overlapping. Examples are adjacent apartments, adjacent states, and adjacent sides of a polygon.The word adjacent as used in the definitions of the cosine and tangent trigonometric functions can be a little confusing because, obviously, it takes two sides to make an angle in a polygon, so, technically, you could say that each angle is adjacent to two sides. When trig functions refer to the side adjacent to one of the acute angles in a right triangle, they are referring to the one that's not the hypotenuse, or, in other words, the one that is also adjacent to the right angle.
Is sine a trig function?
Yes, sine is a trig function, it is opposite over hypotenuse.
What is the trig ratio equal to the opposite side divided by the hypotenuse?
sine
How do you measure cosine?
To find the cosine of an angle, you divide the adjacent side of the triangle by the hypotenuse. A helpful hint for the trig functions of sin, cos, and tan is SOH CAH TOA. It's a helpful way to remember what to do. For Sine you divide the opposite side by the hypotenuse. In Tangent, you divide the opposite side by the adjacent side.
What is the trig ratio which relates the opposite to the adjacent of a triangle?
the tangent of an angle is opposite over adjacent side of triangle
What are the 3 basic trig ratios and how do they work?
The three basic ratios are sine, cosine and tangent.In a right angled triangle,the sine of an angle is the ratio of the lengths of the side opposite the angle and the hypotenuse;the cosine of an angle is the ratio of the lengths of the side adjacent to the angle and the hypotenuse;the tangent of an angle is the ratio of the lengths of the side opposite the angle and the the side adjacent to the angle.
How do you find the hypotenuse when only one length is given?
If the only information you have is the length of one side of a triangle, there are an infinite number of triangles having that length. Since the hypotenuse is defined to be "The side opposite the right angle in a plane right triangle", you will need the length of the other side to find the hypotenuse using the Pythagorean theorem. Alternatively you need to know the other angles. Then you can use the appropriate trig function to find the length of the hypotenuse.
How do you determine the measure of an angle with trig?
Depends on what is given. SOHCAHTOA where O=opposite side, H=hypotenuse, A=opposite sides of a triangle in relation to the angle you are seeking.C=cosine, S=sine, T=tangent. So it depends on what is given and what is sought to be any more specific!
What does sin cos and tan mean?
They are sine, cosine and tangent, three trigonometric functions. There is a mnemonic device to help you remember what these functions represent. Imagine a right triangle (a triangle containing a 90 degree or right angle). We are interested in the two angles that are NOT 90 degrees. When you imagine these angles you can see that on one side will be the hypotenuse, the long side opposite the right angle. The other side of the angle is the adjacent leg for that angle. So either of these angles is made up of the hypotenuse and its adjacent leg. The other side is the opposite leg. Now imagine that a space alien named Soh-cah-toa is teaching you trigonometry. SOH means that the sine is calculated by "opposite over hypotenuse"; the length of the opposite leg divided by the length of the hypotenuse". CAH means that the cosine is calculated by "adjacent over hypotenuse"; the length of the adjacent leg divided by the length of the hypotenuse". TOA means that the tangent is calculated by "opposite over adjacent"; the length of the opposite leg divided by the length of the adjacent leg. If youd like a simpler method, check out these articles for a simple free tool and tutorial that will make trig simple enough for ANYBODY to understand! http://www.ehow.com/how_5520340_memorize-trig-functions-losing-mind.html http://www.ehow.com/how_5227490_pass-mind-part-unknown-sides.html http://www.ehow.com/how_5428511_pass-part-ii-unknown-angles.html
What are good math rhymes?
One to remember the trig ratios:Two Old ArabsSoft Of HeartCoshed Andy HatchetWhich gives:Tan = Opposite / AdjacentSin = Opposite / HypotenuseCos = Adjacent / Hypotenuse[Learnt that when I was about 10-11.]
How do you find an angle of a right-angle triangle when you have all the lengths - using trigonometry?
(the side opposite the angle) divided by (the side adjacent to the angle) = tangent of the angle (the side opposite the angle) divided by (the hypotenuse of the triangle) = sine of the angle (the side adjacent to the angle) divided by (the hypotenuse of the triangle) = cosine of the angle Once you have the sine OR the cosine OR the tangent of the angle, you can get the measurement of the angle on a scientific calculator, or look it up in a table of trig functions in a book. Check out these articles for a simple free tool and tutorial that will make trig simple enough for ANYBODY to understand! http://www.ehow.com/how_5520340_memorize-trig-functions-losing-mind.html http://www.ehow.com/how_5227490_pass-mind-part-unknown-sides.html http://www.ehow.com/how_5428511_pass-part-ii-unknown-angles.html
How do you find the remaining legs of a 45 45 90 isosceles right triangle given a hypotenuse of 48 inches?
trig functions sin(45o) = opposite/hypotenuse sin(45o) = opp/48 inches 48 inches * sin(45o) = opposite = 34 inches ===============you do other side with appropriate trig function Update: Use Pythagoras. Adj^2 + Opp^2 = Hyp^2 (For Isosceles right angles triangle Adj = Opp) Therefore, Adj = Opp = Sqrt((Hyp^2)/2) = 33.9
The hypotenuse of a right triangle is the side opposite the blank?
Check out these articles for a simple free tool and tutorials that will make trig simple enough for ANYBODY to do! http://www.ehow.com/how_5520340_memorize-trig-functions-losing-mind.html http://www.ehow.com/how_5227490_pass-mind-part-unknown-sides.html http://www.ehow.com/how_5428511_pass-part-ii-unknown-angles.html
