Question

Given the value of the hypotenuse c for a 30°-60°-90° triangle, write the equations to represent sides a and b in terms of c. Assume a is the shorter leg.

Answer 1

a = 1/2 • c

b = (root3)/2 • c

Explanation:

30°-60°-90° triangle is a Special Right Triangle. There's a great short cut to find the sides if you know any one side. No trig or Pythagorean Theorem necessary (but that is where the short cut comes from)

The hypotenuse is double the short leg OR the short leg is half the hypotenuse. The long leg is the short leg times the sqroot3. Your question asked for everything in terms of c (the hypotenuse) see image. We can use these shortcuts to find your answer. See image.