Question

find the length of side x to the nearest tenth.
right triangle with one angle 60°, one angle 30°, hypotenuse? no, the side labeled 7 is adjacent to 60°? wait, the right angle, one angle 60°, one 30°, the side between 60° and right angle is 7? wait, the triangle: right angle, 60° at top left, 30° at bottom, the side opposite 30°? wait, the side labeled 7 is the side adjacent to 60°? wait, the side x is opposite 60°? wait, the triangle: vertices: right angle at top right, 60° at top left, 30° at bottom. so the side from top left to top right is 7 (adjacent to 60°), the side from top right to bottom is x (opposite 60°), and the side from top left to bottom is the hypotenuse. so we can use trigonometry: tan(60°) = x / 7, so x = 7 tan(60°). or maybe cos(60°) or sin? wait, angle 60°, adjacent side 7, opposite side x. so tan(theta) = opposite/adjacent, so tan(60°) = x / 7, so x = 7 tan(60°). tan(60°) is √3 ≈ 1.732, so x ≈ 7 1.732 ≈ 12.1? wait, no, wait: maybe i got the angles wrong. wait, in a 30-60-90 triangle, the sides are in ratio 1 : √3 : 2. the side opposite 30° is the shortest, then opposite 60° is √3 times that, hypotenuse is twice. wait, if the angle at the bottom is 30°, then the side opposite 30° is the side adjacent to 60°, which is 7? wait, no: in a right triangle, angle a = 60°, angle b = 30°, right angle c. so side opposite a (60°) is bc, side opposite b (30°) is ac, side opposite c (right angle) is ab (hypotenuse). so if angle at top left is 60° (a), right angle at top right (c), 30° at bottom (b). then side ac is from a to c: length 7 (adjacent to a, since angle at a is 60°, so ac is adjacent, bc is opposite (x), ab is hypotenuse. so tan(a) = bc / ac → tan(60°) = x / 7 → x = 7 tan(60°) ≈ 7 * 1.732 ≈ 12.1. alternatively, if ac is 7 (adjacent to 60°), then bc (x) is opposite 60°, so tan(60°) = x / 7. so the ocr text is: find the length of side x to the nearest tenth. and the triangle as described: right triangle, 60°, 30°, side 7, x.

Explanation:

Step1: Identify trigonometric ratio

We use tangent, as we know the angle $60^\circ$, the side opposite to it is $x$, and the adjacent side is 7. The tangent formula is $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$.
$\tan(60^\circ) = \frac{x}{7}$

Step2: Solve for $x$

Rearrange the formula to isolate $x$, then substitute $\tan(60^\circ) = \sqrt{3} \approx 1.732$.
$x = 7 \times \tan(60^\circ)$
$x \approx 7 \times 1.732$

Step3: Calculate and round

Compute the product and round to the nearest tenth.
$x \approx 12.124 \approx 12.1$

Answer:

12.1