Question

what is the height, x, of the equilateral triangle? triangle with 60° angles, base 14 in., height x options: a. $7\sqrt{3}$ inches, b. 7 inches, c. $14\sqrt{3}$ inches, d. 14 inches, e. $7\sqrt{2}$ inches

Explanation:

Step1: Identify side length

All sides of equilateral triangle are equal, so side length \(s = 14\) inches.

Step2: Split into right triangles

Height splits base into two equal parts: \(\frac{s}{2} = 7\) inches.

Step3: Apply Pythagorean theorem

Height \(x = \sqrt{s^2 - (\frac{s}{2})^2} = \sqrt{14^2 - 7^2}\)

Step4: Calculate value

\(x = \sqrt{196 - 49} = \sqrt{147} = 7\sqrt{3}\) inches.

Answer:

A. \(7\sqrt{3}\) inches