How do you find the length of the hypotenuse and one leg of a right angled triangle, when only 1 angle and the length of the other leg is given?

Question

I need to find the length of a hypotenuse and a leg of a right angled triangle when the only information given are the length of the other leg(28) and 2 angles, the right angle, and the other angle (62.5 degrees).

Answer 1

cos(62.5º)=28/hypotenuse

hypotenuse=28/cos(62.5º)

hypotenuse=28/0.4617486

hypotenuse=60.639

now use the Pythagorean Theorem

(60.639)^2=28^2+n^2 where n=the other leg

3677.088=784+n^2

3677.088-784=n^2

2893.088=n^2

n=√2893.088

n=53.787 is the other leg

 

Answer 2

Hi Jacob.

 

You need to use trig functions.  Recall Sin x = opposite over hypotenuse, Cos x = adjacent over hypotenuse and Tan x = opposite over adjacent.

 

I can't tell you which to start with because you haven't indicated if the leg with a measure of 28 is adjacent to the 62.5 degree angle or opposite. 

 

Hopefully this will help.