Question

select the correct answer.
what is the height, x, of the equilateral triangle?

a. ( 7sqrt{3} ) inches
b. 7 inches
c. ( 14sqrt{3} ) inches
d. 14 inches
e. ( 7sqrt{2} ) inches

Explanation:

Step1: Divide the equilateral triangle

Divide the equilateral triangle into two right - angled triangles. The base of each right - angled triangle is \(\frac{14}{2}=7\) inches.

Step2: Use the Pythagorean theorem or trigonometry

Using the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 14\) (the side of the equilateral triangle) and \(a = 7\) (half of the base). Let the height be \(x\). Then \(x=\sqrt{14^{2}-7^{2}}=\sqrt{(14 + 7)(14 - 7)}=\sqrt{21\times7}=\sqrt{147}=7\sqrt{3}\).
Alternatively, using trigonometry \(\sin60^{\circ}=\frac{x}{14}\), since \(\sin60^{\circ}=\frac{\sqrt{3}}{2}\), then \(x = 14\times\frac{\sqrt{3}}{2}=7\sqrt{3}\).

Answer:

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