Question

The triangle below is equilateral . Find the length of side x in simplest radical form with a rational denominator . The image is below.

Answer 1

Explanation:

See diagram below

Remember for a RIGHT triangle sin = opposite leg / hypotenuse

so for the red highlighted triangle sin 60 = 5 / x

or x = 5 / sin 60

= 5/ ( sqrt(3) / 2) = 10 / sqrt 3 = 10 sqrt (3) / 3

Answer 2

triangle equilateral

the height resulting from a vertex is the median of the side opposite this vertex

the height forms a right triangle

x²=(x/2)²+5²

x²=(x²/4)+25

4x²/4 =(x²+100)/4

4x²=x²+100

4x²-x²=100

3x²=100

x²=100/3

x=V(100/3) = 10/V3 = 10V3/3