Question

solve for x. round to the nearest tenth, if necessary.
answer attempt 1 out of 2
x =

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \(NML\), we know the adjacent side (\(ML = 52\)) to the angle \(L=20^{\circ}\) and we want to find the hypotenuse (\(NL=x\)). The cosine ratio is defined as \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(20^{\circ})=\frac{ML}{NL}\).

Step2: Solve for \(x\)

Substitute \(ML = 52\) and \(NL=x\) into the cosine formula: \(\cos(20^{\circ})=\frac{52}{x}\). Then, we can solve for \(x\) by cross - multiplying: \(x=\frac{52}{\cos(20^{\circ})}\).
We know that \(\cos(20^{\circ})\approx0.9397\). So, \(x=\frac{52}{0.9397}\approx55.3\).

Answer:

\(55.3\)