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How do you find the hypotenuse with only a leg and a degree?
It depends on the position of the 'leg' compared to the known angle. If the 'leg' makes up one of the two sides of the angle, then the other side of the angle is the hypotenuse. In this case the 'leg' would be referred to as the 'adjacent' side. The side the doesn't form part of the angle is referred to as the 'opposite' side. So using the trig. functions. Sin(angle) = opposite / hypotenuse. Then algebraically rearranging hypotenuse = opposite / Sin(angle). Similarly for 'Cos'. Cos(angle) = adjacent/ hypotenuse Hence Hypotenuse = adjacent / Cos(angle) So as an example If the leg/opposite is 2 units. and the angle 30 degrees. Then hypotenuse = 2 / Sin(30). On you calculator you should be find the Sin( 30) = 1/2 = 0.5 Substitute in hypotenuse = 2 / 1/2 ( That is '2' divided by '1/2'), (Division of fractions). hypotenuse = 2 X 2/1 = 4/1 = 4 units. NB When using your calculator to find 'Sin' , 'Cos', and 'Tan' of angles, you will read out some 'horrible' decimal numbers. NNB Do NOT use the TAN(gent) function to find hypotenuse. It is NOT part of the Tan ratio. Here is an 'aide memoire' for the Trig . functions. SOH , CAH, TOA. ( Said as 'soccatoa'). SOH = Sin(angle) = opposite/ hypotenuse = o/h CAH = Cos(angle) = adjacent/hypotenuse = a/h TOA = Tan(Angle) = opposite/adjacent = o/a
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 hypotenuse if you know one leg and one angle?
Remember the Trig. Functions. Sin(Angle) = opposite / hypotenuse. Hence algebraically rearranging. hypotenuse = opposite / [Sin(angle)) NB You MUST know the length of the 'opposite', and the size of the angle. So if the opposite is of length '2' and the angle is 30 degrees. Then substituting ;= hypotenuse = 2 / Sin(30) From Tables or calculator 'Sin(30) = 1/2 = 0.5' Hence hypotenuse = 2 / (1/2) or 2/(0.5) 2/(1/2) = 4 or 2/0.5 = 4 Hence the hypotenuse is '4' units in length.
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.
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
What does tan equal in trigonometry?
Tan = o/a Tangent of an angle = opposite over adjacent. Here are the other Trig. functions. SINe(angle) = opposite/hypotenuse COSine(angle) = adjacent/hypotenuse COTangent(angle) = adjacent/opposite Cosecant(CSC)(angle) = hypotenuse/oppositre SECant(angle) = hypotenuse/ adjcent.
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.
Formula for finding the hypotenuse of a triangle?
Two methods ;- #1 ; Use Pythagoras, if the lengths of the other two sides are known. h^(2) = s(1)&(2) + s(2)^(2) In words, 'The hypotenuse squared is the sum of the squares of the other two sides. #2 ; Use Trigonometry (trig.) is the length of one side and an angle are known . Hence Sin(angle) = opposite / hypotenuse hypotenuse = opposite / Sin(angle) or Cos(angle) = adjacent/hypotenuse hypotenuse = adjacent/Cos(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
