Question

solve for x. round to the nearest tenth, if necessary.
(image of a right triangle pqo with right angle at p, pq = 33, angle at o is 19 degrees, and po = x)
answer attempt 1 out of 2
x = |

Explanation:

Step1: Identify trigonometric ratio

In right triangle \( \triangle OPQ \), \( \angle O = 19^\circ \), opposite side to \( \angle O \) is \( PQ = 33 \), adjacent side is \( OP = x \). So we use \( \tan\theta=\frac{\text{opposite}}{\text{adjacent}} \), here \( \tan(19^\circ)=\frac{33}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{33}{\tan(19^\circ)} \). Calculate \( \tan(19^\circ)\approx0.3443 \), then \( x=\frac{33}{0.3443}\approx95.8 \).

Answer:

\( 95.8 \)