Question

14 points!

Find the missing length of the sides.

Please explain every step so that I may learn how to do this.
Thank you in advance!

Answer 1

In a 30-60-90 triangle the side opposite the 30 degree angle is half the length of the hypotenuse ⇒ a = 6/2 = 3 in.

By the Pythagorean theorem:
b = √(6² - 3²) = √(36-9) = √27 = 3√3 in.

Answer: a=3 in, b=3√3 in.