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The length of the hypotenuse works out as 17 miles

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Q: The legs of a right triangle measures 8 miles and 15 miles what is the length of the hypotenuse?
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The perimeter of a triangle with equal sides is 36 miles what is the length of each side?

The length of each side of the triangle is 12 miles.


How many miles in 1 square miles?

That's not a valid question. A mile measures length, a square mile measures area.


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.


Which is greater 450 miles or 850 square miles?

They ate two different types of measurement. Miles measures length and square miles measures area and you cannot convert between the two.


If the Bermuda triangle has a perimeter of 3075 miles shortest side measures 75 mi less than the middle side longest side measures 375 mi more than the middle side find the length of the three sides?

m = middle side lengthshortest side length is 75 miles less than the middle side length m; so, use (m - 75) to represent the length of the shortest sidelongest side length is 375 miles longer than the middle side length m; so, us (m + 375) to represent the length of the longest sideperimeter of the triangle = the sum of all the side lengths3075 = m + (m - 75) + (m + 375)3075 = 3m + 3002775 = 3m925 = m3075 = 925 + (925 - 75) + (925 + 375)Therefore, the lengths of the sides from smallest side to longest side are: 850 miles, 925 miles, and 1300 miles


What is measured in meters miles and light years?

Those are all measures of length.


The distance between A and C is 60 miles and the distance between A and B is 50 miles and the distance between B and C is 50 miles. What is the distance from B to the straight line between A and C?

Draw an isosceles triangle with a base A-C of length 60. The apex of the triangle, point B, is length 50 from both point A and point C. That's your triangle. Drop a "vertical" from B to the base - where it will form a right angle with that line segment and, because the sides are the same length, will bisect the base. That's the line segment you're looking to find the length of. So let's. The base, length 60, is divided into two equal segments by the vertical. That's two length-30 pieces. Notice that your figure, the isosceles triangle with that vertical drawn in, is two "back-to-back" right triangles, each with a base of length 30 and a hypotenuse of length 50. We can "cheat" here and see that the triangles have sides of length 30, 40 and 50. We also know that 3, 4, 5 is a "magic" right triangle because 32 + 42 = 52 (9 + 16 = 25). Our triangle in this problem has sides (conveniently) ten times the length of the 3, 4, 5 triangle. That makes them 30, 40 and 50 in length. The height of the triangle is 40 miles. If you want to work it through, 302 + h2 = 502 900 + h2 = 2500 h2 = 2500 - 900 = 1600 = 40 Our work checks.


What appropriate unit to measure the length of highway is?

Miles or Kilometers are the usual measures of distance when dealing with highways and roads.


If two planes leave the same airport at 1 o'clock PM how many miles apart will they be at 3 o'clock PM if one travels directly north at 150 mph and the other travels directly west at 200 mph?

One plane will be 300 miles (150 mph * 2hours ) north. The other plane will be 400 miles (200 mph * 2hours ) west. This makes a right triangle with sides of 300 and 400. If you know your right triangles, you will know that the hypotenuse will be 500 miles. (3-4-5 triangle) If not hypotenuse = √(3002+4002) = 500 miles They will be 500 miles apart.


What is the smallest state is in the us?

Rhode Island is the smallest state in the U.S. It only measures about 30 miles in length.


What is the distance across Turkey?

The Republic of Turkey measures some 400+ miles across its length. From top to bottom Turkey has a distance of approximately 990+ miles.


How many miles are in 5.0 liters?

Miles is a measurement of length and liters measures liquids. They cannot be compared. Miles can be compared to kilometers, meters, centimeters, etc., and the most common comparison is miles to kilometers.