Question

Find the tangent of angle S. Reduce the answer to the lowest terms.

Answer 1

To answer this question, we can proceed as follows:

1. We have a right triangle here. Then we can use trigonometric ratios. These trigonometric ratios are sine, cosine, tangent, secant, cosecant and cotangent.

2. We need to identify the reference angle, in this case, angle S.

3. We have to identify the opposite side to this angle, and the adjacent side to this angle too.

4. The hypotenuse is the largest side of the triangle, in this case, the side RS.

5. We also know that the tangent is given by:

`\tan (\theta)=(opposite)/(adjacent)`

That is the ratio between the opposite side of the angle to the adjacent side of the angle.

6. Then we have:

We can see that the opposite side to angle S is the one in front of the angle. In this case, the side RT is equal to 9. The adjacent side is ST = 12 - this side is near to the angle S.

Finally, therefore, the tangent of angle S will be:

`\begin{gathered} \tan (\angle S)=\frac{\text{opp}}{\text{adj}} \\ \tan (\angle S)=(9)/(12)=((9)/(3))/((12)/(3))=(3)/(4) \\ \tan (\angle S)=(3)/(4) \end{gathered}`

In summary, therefore, the tangent of angle S is equal to (reduced to the lowest terms):

`\tan (\angle S)=(3)/(4)`