Question

question
the triangle below is equilateral. find the length of side x to the nearest tenth.
(image of an equilateral triangle with a perpendicular segment of length 5 creating a right triangle with side x)

Explanation:

Step1: Identify triangle properties

The triangle is equilateral, so all angles are 60°. The segment of length 5 is adjacent to a 60° angle in a right triangle.

Step2: Use cosine function

$\cos(60^\circ) = \frac{5}{x}$

Step3: Solve for x

$x = \frac{5}{\cos(60^\circ)} = \frac{5}{0.5} = 10$? No, wait—correction: If the right triangle has hypotenuse as the side of the equilateral triangle, and 5 is opposite 30°? Wait, standard equilateral triangle height splits it into 30-60-90. If 5 is the shorter leg (opposite 30°), then hypotenuse $x = 2×5 = 10$? No, wait the diagram shows a right triangle with one leg 5 and hypotenuse x, angle at hypotenuse end is 60°: $\sin(60^\circ)=\frac{5}{x} → x=\frac{5}{\sin60^\circ}=\frac{5}{\sqrt{3}/2}≈5.77≈5.8$

Step4: Round to nearest tenth

$x≈5.8$

Answer:

5.8