Question

question
the triangle below is equilateral. find the length of side x to the nearest tenth.
(image of an equilateral triangle with a height splitting it into two right triangles, one leg labeled 3, the other leg labeled x)
answer attempt 1 out of 2
x =
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Explanation:

Step1: Identify triangle properties

The triangle is equilateral, so all sides = 3, and all internal angles = $60^\circ$. The segment $x$ is a perpendicular (height) from a vertex to the opposite side.

Step2: Use sine for right triangle

In the right triangle formed by side 3, $x$, and half the base, $\sin(60^\circ) = \frac{x}{3}$.

Step3: Solve for $x$

$x = 3 \times \sin(60^\circ) = 3 \times \frac{\sqrt{3}}{2}$

Step4: Calculate decimal value

$x = \frac{3\sqrt{3}}{2} \approx 3 \times 0.8660 \approx 2.6$

Answer:

$2.6$