SOLUTION: I have a 30-60-90 triangle, and the long leg is 33 degrees. How do I find the short leg and hypotenuse?

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Question 701683: I have a 30-60-90 triangle, and the long leg is 33 degrees. How do I find the short leg and hypotenuse?
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

A 30-60-90 triangle is a right triangle whose internal angles are 30,+60 and 90+degrees.
The three sides of a 30-60-90 triangle have the following characteristics:
All three sides have different lengths.
The shorter leg,+b, is half the length of the hypotenuse, c. That is,
b=c%2F2
The longer leg's length, a, is the shorter leg times sqrt%283%29. That is,
a=b+%2Asqrt%283%29
so, you are given c=33
then, you have the shorter leg +b=c%2F2...=>...+b=33%2F2...=>...+b=16.5
and the longer leg's length is a=b%2Asqrt%283%29..=>...+a=16.5%2A1.7321...=>...+a=28.545
check result using Pythagorean theorem:
c%5E2=a%5E2%2Bb%5E2
33%5E2=28.58%5E2%2B16.5%5E2
1089=816.8164%2B272.25
1089=1089.0664...round decimal to whole number
1089=1089

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
I have a 30-60-90 triangle, and the long leg is 33 degrees. How do I find the short leg and hypotenuse?

When the longer leg of a 30-60-90 triangle is known, its shorter leg = longer_leg%2Fsqrt%283%29, or in this case: 33%2Fsqrt%283%29 ----- %2833sqrt%283%29%29%2F%28sqrt%283%29+%2A+sqrt%283%29%29 ---- 33sqrt%283%29%2F%28sqrt%289%29%29 ----- 33sqrt%283%29%2F3 ----- 11cross%2833%29sqrt%283%29%2Fcross%283%29 ----- 11sqrt%283%29, or highlight_green%2819.05255888%29

When the longer leg of a 30-60-90 triangle is known, its hypotenuse = 2%28longer_leg%2Fsqrt%283%29%29, or in this case: 2%2A11sqrt%283%29, or 22sqrt%283%29, or 2 *19.05255888 ≈ highlight_green%2838.1%29

You can do the check!!

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