Question

Need help please! The height of the equilateral triangle below is 15 units. What is the value of x?

a) 15 sqrt 3
b)30 sqrt 3
c)15/sqrt 3
d)30/sqrt 3

Answer 1

The answer b or 30 sqrt 3

Explanation:

Answer 2

The equilateral triangle may be splited into two congruent isosceles right triangles, each with height 15, and angles 30°-60°-90°.

Then you have this ratios:

tan (60) = height / [base of the equilateral triangle / 2] => base = 2*15 / tan(60) = 30/√3

sin (60) = height / hypothenuse => hypothenuse = height / sin(60) = 15 / [√3 / 2] = 30 / √3.

Same result of above which is right because the three sides are equals.

Then, side of the equilateral triangle is 30 / √3