Question

solve for x. round to the nearest tenth, if necessary. triangle jik with right angle at j, ji = 4.6, jk = x, angle at k is 42°

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle JKI \), \( \angle K = 42^\circ \), opposite side to \( \angle K \) is \( JI = 4.6 \), adjacent side is \( JK = x \). We use \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \), so \( \tan(42^\circ)=\frac{4.6}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{4.6}{\tan(42^\circ)} \). Calculate \( \tan(42^\circ)\approx0.9004 \), then \( x=\frac{4.6}{0.9004}\approx5.1 \).

Answer:

\( 5.1 \)