Question

the triangle below is equilateral. find the length of side $x$ to the nearest tenth.
(an image of an equilateral triangle with a height drawn, forming a right triangle with one leg $x$ and hypotenuse 12)
answer attempt 2 out of 2
$x = \boxed{10.4}$ (with a calculator interface shown)

Explanation:

Step1: Define equilateral triangle property

All sides = 12, right triangle formed.

Step2: Use sine for adjacent side

$\sin(60^\circ) = \frac{x}{12}$

Step3: Solve for x

$x = 12 \times \sin(60^\circ) = 12 \times \frac{\sqrt{3}}{2} = 6\sqrt{3}$

Step4: Calculate decimal value

$6\sqrt{3} \approx 6 \times 1.732 = 10.392$

Step5: Round to nearest tenth

$10.392 \approx 10.4$

Answer:

$x = 10.4$