Question

solve for x. round to the nearest tenth, if necessary.
triangle image with right angle at n, side no = 7, angle at o is 52°, side nm = x

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle NOM \), \( \angle O = 52^\circ \), \( ON = 7 \) (adjacent to \( \angle O \)), and \( x = MN \) (opposite to \( \angle O \)). We use the tangent ratio: \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \). So, \( \tan(52^\circ)=\frac{x}{7} \).

Step2: Solve for \( x \)

Multiply both sides by 7: \( x = 7\times\tan(52^\circ) \). Calculate \( \tan(52^\circ)\approx1.2799 \), then \( x\approx7\times1.2799\approx8.9593 \). Round to nearest tenth: \( x\approx9.0 \).

Answer:

\( x \approx 9.0 \)