# math

If the short leg of a 30-60-90 right triangle is 2 feet. What is the long leg and the hypotenuse?

My answer: Long leg = 2 feet
Hypotenuse = 4 feet

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1. no, you have to use trig, or else know that the ratio of sides of the 30-60-90 triangle is
1:√3:2
So if the short side is 2, the sides are:
2 : 2√3 : 4

or
make a sketch, mark the shortest side adjacent to the 60° angle as 2 and the hypotenuse as h
cos60° = 2/h
h = 2/cos60 = 4
now use Pythagoras to find the side opposite the 60° angle,
2^2 + x^2 = 4^2
4 + x^2 = 16
x^2 = 12
x = √12 = 2√3 , same as above

btw,
2^2 + 2^2 ≠ 4^2, so you would not have a right-angled triangle with your sides

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posted by Reiny

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