Question

using trig to find a side
score: 0/5 penalty: 1 off
question
solve for x. round to the nearest tenth, if necessary.
answer attempt 1 out of a
x=
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Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle MNL\) with right - angle at \(M\), we know the side \(ML = 80\) and the angle \( \angle L=59^{\circ}\). We want to find the side \(x\) (adjacent to the angle \( \angle L\)). We use the cosine function. The cosine of an angle in a right - triangle is defined as \( \cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \( \theta = 59^{\circ}\), adjacent \(=x\), and hypotenuse \(=NL\). But we can also use the fact that \( \cos(59^{\circ})=\frac{ML}{NL}\) is incorrect. Wait, no, using \( \sin(59^{\circ})=\frac{MN}{NL}\) and \( \cos(59^{\circ})=\frac{ML}{NL}\) is wrong. Wait, for the angle \( \angle L = 59^{\circ}\), \(\sin(59^{\circ})=\frac{MN}{NL}\), \(\cos(59^{\circ})=\frac{ML}{NL}\), \(\tan(59^{\circ})=\frac{MN}{ML}\). But we can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) (where \(a = MN\), \(b = ML = 80\), \(c = NL=x\)) is wrong. Wait, no, we should use \( \cos(59^{\circ})=\frac{ML}{NL}\). Rearranging for \(NL\) (since \(ML = 80\)), \(NL=\frac{ML}{\cos(59^{\circ})}\).

Step2: Calculate the value

We know that \( \cos(59^{\circ})\approx0.515\) (using a calculator). Then \(x=\frac{80}{\cos(59^{\circ})}\). Substitute the value of \( \cos(59^{\circ})\): \(x=\frac{80}{0.515}\approx155.3\).

Answer:

\(155.3\)