Question

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

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle \( \triangle MLN \) with \( \angle M = 90^\circ \), \( ML = 80 \), \( \angle L = 59^\circ \), and hypotenuse \( NL = x \). We use the cosine ratio, which is \( \cos(\theta)=\frac{\text{adjacent}}{\text{hypotenuse}} \). Here, \( \cos(59^\circ)=\frac{ML}{NL}=\frac{80}{x} \).

Step2: Solve for \( x \)

Rearranging the formula for \( x \), we get \( x = \frac{80}{\cos(59^\circ)} \). Calculate \( \cos(59^\circ) \approx 0.5150 \). Then \( x=\frac{80}{0.5150}\approx155.3 \).

Answer:

\( 155.3 \)