Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify the trigonometric ratio

In right triangle \( \triangle NOP \), \( \angle O = 90^\circ \), \( \angle P = 23^\circ \), \( OP = 36 \), and \( NP = x \) (hypotenuse). We use the cosine function, which is \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). Here, \( \cos(23^\circ)=\frac{OP}{NP}=\frac{36}{x} \).

Step2: Solve for \( x \)

Rearrange the formula: \( x = \frac{36}{\cos(23^\circ)} \). Calculate \( \cos(23^\circ) \approx 0.9205 \). Then \( x=\frac{36}{0.9205}\approx 39.1 \).

Answer:

\( 39.1 \)