Question

I need help finding the answerA. 31.6B. 23.6C. 31.1D. 20.9

Answer 1

First, notice that we have two right triangles, the one to the left and the one to the right. The bigger one is no a right triangle.

In right triangles, we can use sine, cosine and tanget to relate their side measures and angles measures.

Both right triangles share one side, the blue one. We don't have enough information to calculate x at the start, but if we knew the measure of the blue side we could.

Using the triangle to the left, we can us tanget of the indicates angles, 58°, to relate the opposite leg, 29, and the adjacent leg, the blue side.

Let the blue side be y, then:

`\begin{gathered} \tan 58\degree=(29)/(y) \\ y=(29)/(\tan 58\degree) \\ y=(29)/(1.60033\ldots) \\ y=18.1212\ldots \\ y\approx18.1 \end{gathered}`

Now, we can use sine of 50° on the triangle to the right to relate the opposite leg, y, and the hypotenuse, x:

`\begin{gathered} \sin 50\degree=(y)/(x) \\ x=(y)/(\sin 50\degree) \\ x=(18.1)/(0.7660\ldots) \\ x=23.627\ldots \\ x\approx23.6 \end{gathered}`

This matches alternative B.