Question

Find the length of side x in simplest radical form with a rational denominator.
30°
60°
x
11
Answer
Attempt 1 out of 2

Answer 1

In a 30°-60°-90° triangle the sides are in the ratio 1 : √3 : 2 (opposite 30°, 60°, hypotenuse). If the side opposite 60° is 11 and x is the side opposite 30°, then

x / 11 = 1 / √3 ⇒ x = 11 / √3.

Rationalize the denominator: x = (11√3) / 3.

Answer: (11√3)/3.