Question

A * XD Trig Ratios Practice 4 POSSIBLE POINTS: 1 27 38 In the above triangle, would you use SINE, COSINE, or TANGENT to solve for the missing side (TYPE IN ALL CAPS)? The measure of the missing angle is (ROUND TO THE NEAREST DEGREE). 1 2 3 4 5 6 7 8 9

Answer 1

SINE, COSINE

35°

Explanation:

We know the opposite and adjacent legs of the triangle, therefore, we can calculate the value of the missing side, which is the hypotenuse by means of sine and cosine, since both trigonometric ratios include the hypotenuse.

`\begin{gathered} \sin \theta=\frac{\text{opposite}}{\text{hypotenuse}} \\ \cos \theta=\frac{\text{adjacent}}{\text{hypotenuse}} \end{gathered}`

To calculate the angle, we must use the tangent trigonometric ratio that relates both legs, like this:

`\begin{gathered} \tan \theta\: =\: (27)/(38) \\ \theta=\arctan \mleft((27)/(38)\mright) \\ \theta=35.39\cong35\text{\degree} \end{gathered}`