Question

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

Answer 1

Answer:

x = 8

Step-by-step explanation:

If a triangle is equilateral, each vertex has an angle that is equal to 60 degrees

As we can see, we have two sets of similar right triangles

The value x faces the right angle and that makes it the hypotenuse

Also, the side measure 4 is the adjacent side to the angle 60

The trigonometric identity that relates the hypotenuse and the adjacent is the cosine

it is the ratio of the adjacent to the hypotenuse

Mathematically;

cos 60 = 4/x

x = 4/cos 60

x = 8