Question

solve for x. round to the nearest tenth, if necessary.
image of a right triangle opq with right angle at p, pq = 8, angle at q is 75 degrees, and hypotenuse oq is labeled x
answer attempt 1 out of 2
x = input box submit answer

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( OPQ \), \( \angle Q = 75^\circ \), \( PQ = 8 \) (adjacent side to \( \angle Q \)), and \( x = OQ \) (hypotenuse). We use the cosine ratio: \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). So, \( \cos(75^\circ)=\frac{8}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{8}{\cos(75^\circ)} \). Calculate \( \cos(75^\circ)\approx0.2588 \). Then \( x=\frac{8}{0.2588}\approx30.9 \).

Answer:

\( 30.9 \)