Question

Which trig function would you use to solve each 1?

Answer 1

Step 1. The first step is to remember the definitions for the sine, cosine, and tangent for right triangles:

`\begin{gathered} \cos A=\frac{\text{adjacent side}}{\text{hypotenuse}} \\ \sin A=\frac{\text{opposite side}}{\text{hypotenuse}} \\ \tan A=\frac{\text{opposite side}}{\text{adjacent side}} \end{gathered}`

Where A is the angle, the opposite side is the opposite side to this angle, the adjacent side is the side adjacent to this angle, and the hypotenuse is the side opposite to the 90° angle.

This is all summarized in the following diagram:

Step 2. For the first triangle, we know one angle, we are looking for the opposite side, and we also know the adjacent side.

The trigonometric function that relates all of these three: Angle, opposite side, and the adjacent side, is the tangent:

`\tan 32=(x)/(13)`

Step 3. For the second triangle, we know the angle, the hypotenuse of 11, and we are looking for the adjacent side x.

The trigonometric function that relates these three: angle, hypotenuse and the adjacent side is the cosine:

`\cos 60=(x)/(11)`

Step 4. For the third

Answer:

First triangle: Tangent

Second triangle: Cosine