Question

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

(image of a right triangle mln with right angle at m, ml = 80, angle at l is 59 degrees, and hypotenuse nl = x)

answer attempt 1 out of 2

Explanation:

Step1: Identify triangle type and trigonometric ratio

We have a right - triangle \( \triangle MLN \) with \( \angle M = 90^{\circ} \), \( ML = 80 \), \( \angle L=59^{\circ} \), and hypotenuse \( x = LN \). We use the cosine function, where \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}} \). For \( \angle L \), the adjacent side to \( \angle L \) is \( ML \) and the hypotenuse is \( LN \). So \( \cos(59^{\circ})=\frac{ML}{LN} \), or \( \cos(59^{\circ})=\frac{80}{x} \).

Step2: Solve for \( x \)

From \( \cos(59^{\circ})=\frac{80}{x} \), we can re - arrange the formula to solve for \( x \). Cross - multiplying gives us \( x=\frac{80}{\cos(59^{\circ})} \). We know that \( \cos(59^{\circ})\approx0.5150 \). Then \( x = \frac{80}{0.5150}\approx155.3 \) (rounded to the nearest tenth).

Answer:

\( 155.3 \)