Question

The triangle below is equilateral. Find the length of side x in simplest radical form

with a rational denominator.

Answer 1

x = √30

Explanation:

For an equilateral triangle, the measure of the angle at each vertex is 60 degrees

Thus, the angle 60 faces the side measure x

Also, the given length is adjacent to the angle 60 measure

Mathematically, the trigonometric ratio that links the adjacent and the opposite is the tan

The tan is the ratio of the opposite to the adjacent

Thus;

Tan 60 = x/ root 10

x = root 10 * tan 60

x √(10 * √(3

x = √30