Question

13 Find the measure of 0. (to the nearest tenth) A) 16.2° B) 16.8° C) 17.1° D) 17.9°

Answer 1

To answer this question, we need to take care that we have a right triangle. In this case, we can use the trigonometric ratios, such as sine, cosine, tangent (at least).

We also need to take care of the reference angle. In this case, the reference angle is theta. We also have the measure of the opposite side of theta, and the measure of the length of the hypotenuse.

Therefore, we can use sine of the angle, since:

`\sin (\theta)=(opp)/(hyp)`

That is the opposite side divided by the measure of the length of the hypotenuse. Then, we have:

`\sin (\theta)=(4)/(13)`

However, to find the measure of the angle we need to use the inverse function of the sine, that is, the arcsine or sin^-1:

`\sin ^(-1)(\sin (\theta))=\sin ^(-1)((4)/(13)_{})`

Then, we have:

`\theta=\sin ^(-1)((4)/(13))\Rightarrow\theta=17.9202131394`

Thus, rounded this value to the nearest tenth, we have that:

`\theta=17.9^(\circ)`

Therefore, the correct answer is option D (17.9 degrees).