Question

question
find the length of side ( x ) to the nearest tenth.
(right triangle with angles 30°, 60°, right angle; side opposite 30°? wait, no, the triangle has a right angle, one angle 30°, one 60°, side labeled 12 (hypotenuse? wait, the side between 30° and right angle is 12? wait, the triangle: right angle, 30° at top, 60° at bottom, side labeled 12 is the hypotenuse? wait, the side labeled 12 is between the 30° angle and the right angle? wait, the triangle diagram: right angle at left, 30° at top, 60° at bottom, side of length 12 is from top (30°) to right angle, and side ( x ) is from top (30°) to bottom (60°)? wait, no, the ocr text: the problem is to find side ( x ), with the triangle having a right angle, 30°, 60°, and side 12. lets re-express: the question is \find the length of side ( x ) to the nearest tenth.\ with a right triangle, angles 30°, 60°, right angle, and one side 12 (probably the hypotenuse or a leg).

Explanation:

Step1: Identify angle and hypotenuse

Hypotenuse = 12, angle = 30°; x is adjacent side.

Step2: Use cosine function

$\cos(30^\circ) = \frac{x}{12}$

Step3: Solve for x

$x = 12 \times \cos(30^\circ) = 12 \times \frac{\sqrt{3}}{2} = 6\sqrt{3} \approx 10.4$

Answer:

10.4