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Find the measure of the hypotenuse of a 30-60-90 triangle whose longer leg has a measure of 6 meters?
Stardustx
The side lengths of a 30-60-90 triangle are always related in this way: the shortest side, measuring x, is opposite the 30 degree angle. The longest side, the hypotenuse, measuring 2x, is opposite the right angle. The third side, measuring xsqrt3, is opposite the 60 degree angle.
In this problem, the side measuring xsqrt3 is 6 meters. If you solve for x, x = 6/sqrt3. The hypotenuse is twice that length, or 12/sqrt3. Normally when you have a square root in the denominator of a fraction you rationalize the denominator to remove the radical from it. If you multiply 12/sqrt3 by sqrt3/sqrt3 and reduce it you get an answer of 4sqrt3.
You can always use the Pythagorean Theorem to check your answers with right triangles. The square of the hypotenuse equals the sum of the squares of the other two sides. In this case, the answer checks.
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Why is the hypotenuse?
The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is always longer than the other two sides of the triangle. This is because the length of the hypotenuse is determined by the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
A right triangle has one side that is 7 cm longer than its shortest side. The triangle’s hypotenuse is 8 cm longer than the shortest side. What are the dimensions of the triangle?
extra 6 dimensions of 10 dimensional spacetime
What are the lengths of the longer leg and the hypotenuse if the shorter leg is 10 on a 30-60-90 triangle?
The short side will be opposite the 30 degree angle. The longer leg is 10*sqrt(3) = 17.32 and the hypotenuse is 20.
Why will sine or cosine never get over one as a decimal?
The sine and the cosine of an angle are both (the leg of a right triangle) divided by (the hypotenuse of the same triangle). The leg can't be longer than the hypotenuse, so this fraction can't be more than ' 1 '.
The length of the hypotenuse of a triangle is 20 what is the shorter leg?
You need to know something else to solve: either the long leg or the angle edit: if it is a right triangle you can use a theorem to figure out the other sides. the smallest side is a, the hypotenuse is 2a, the longer leg is a * sqrt (3) if the hypotenuse is 20, the smaller leg is 10.
Can a leg of a right triangle be longer than the hypotenuse?
No.
How do you use the word hypotenuse in a sentence?
A hypotenuse is the longer and slanting side of a right triangle. So based on that here are some sentences made by yours truly! :) "The hypotenuse of this triangle is 36, correct?" Colleen verified, her voice unsure. Pointing at the overhead projector, Mr. Franco said,"This longer side of this right triangle is called the hypotenuse; For more information, please see your textbook. "
Why is the hypotenuse?
The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is always longer than the other two sides of the triangle. This is because the length of the hypotenuse is determined by the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides.
What is the length of the longer leg of a 30-60-90 triangle to the length of its hypotenuse?
23
What is true of all hypotenuse compared to the other side?
The hypotenuse of any right triangle is longer than either one of the other two sides of the same right triangle. But it's shorter than their sum.
How do you find the length of the sides of a right triangle when you know the hypotenuse?
If it is a 45-45-90 triangle, then divide the hypotenuse by the square root of 2. If it is a 30-60-90 triangle, then the shorter leg would be the hypotenuse divided by 2. And the longer leg would be the the shorter leg multiplied by the square root of 3.
What could be the ratio of the length of of the longer leg of a 30 60 90 triangle to the length of its hypotenuse?
In a 30° 60° 90° triangle, the ratio (long leg)/hypotenuse = sqrt(3)/2 ~ 0.866The ratio (short leg)/hypotenuse = 1/2 = 0.5
Can a right angle triangle ever be equilateral?
No it can't. The hypotenuse of a right triangle will always be longer than either one of the other two sides.
A right triangle has one side that is 7 cm longer than its shortest side. The triangle’s hypotenuse is 8 cm longer than the shortest side. What are the dimensions of the triangle?
extra 6 dimensions of 10 dimensional spacetime
A 30- 60- 90 triangle has a hypotenuse of length 8.6 What is the length of the longer of the two legs?
7.44 - 7.45
What are the lengths of the longer leg and the hypotenuse if the shorter leg is 10 on a 30-60-90 triangle?
The short side will be opposite the 30 degree angle. The longer leg is 10*sqrt(3) = 17.32 and the hypotenuse is 20.
How do you find the hypotenuse and longer leg of a 30 60 90 triangle?
If you have the shorter legs length, then for the hypotenuse, just multiply the shorter leg by 2. For the longer leg, multiply the shorter leg by the square root of 3.
