The hypotenuse of a 30°- 60°- 90° right triangle measures 22 cm. What are the lengths of the longer leg and shorter leg?

Nov 14, 2015

Solve right triangle knowing hypotenuse = 22

Ans: 11 and 19,03

Explanation:

Call A the right triangle with $A = {30}^{\circ}$ and a the opposite side.
We have:
$\sin A = \sin {30}^{2} = \frac{a}{22} - \to a = 22 \sin 30 = 22 \left(\frac{1}{2}\right) = 11$
$\cos A = \frac{b}{22} \to b = 22 \cos 30 = 22 \left(\frac{\sqrt{3}}{2}\right) = 22 \left(\frac{1.73}{2}\right) = 19.03$