Question

1. cos z
2. cos x
3. cos a
4. tan a
5. sin a
6. tan c
7. sin x
8. tan z
9. tan a
10. sin c
11. cos c
12. cos x

Explanation:

Step1: Recall trigonometric - ratio definitions

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, and $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Solve 9) $\cos Z$

For the right - triangle with sides 10, 24, and 26, the side adjacent to $\angle Z$ is 10 and the hypotenuse is 26. So, $\cos Z=\frac{10}{26}=\frac{5}{13}$.

Step3: Solve 10) $\cos X$

For the right - triangle with sides 18, 24, and 30, the side adjacent to $\angle X$ is 24 and the hypotenuse is 30. So, $\cos X=\frac{24}{30}=\frac{4}{5}$.

Step4: Solve 11) $\cos A$

For the right - triangle with sides 12, 35, and 37, the side adjacent to $\angle A$ is 35 and the hypotenuse is 37. So, $\cos A=\frac{35}{37}$.

Step5: Solve 12) $\tan A$

For the right - triangle with sides 5, 12, and 13, the side opposite to $\angle A$ is 5 and the side adjacent to $\angle A$ is 12. So, $\tan A=\frac{5}{12}$.

Step6: Solve 13) $\sin A$

For the right - triangle with sides 9, 12, and 15, the side opposite to $\angle A$ is 9 and the hypotenuse is 15. So, $\sin A=\frac{9}{15}=\frac{3}{5}$.

Step7: Solve 14) $\tan C$

For the right - triangle with sides 24, 32, and 40, the side opposite to $\angle C$ is 24 and the side adjacent to $\angle C$ is 32. So, $\tan C=\frac{24}{32}=\frac{3}{4}$.

Step8: Solve 15) $\sin X$

For the right - triangle with sides 15, 36, and 39, the side opposite to $\angle X$ is 15 and the hypotenuse is 39. So, $\sin X=\frac{15}{39}=\frac{5}{13}$.

Step9: Solve 16) $\tan Z$

For the right - triangle with sides 18, 24, and 30, the side opposite to $\angle Z$ is 18 and the side adjacent to $\angle Z$ is 24. So, $\tan Z=\frac{18}{24}=\frac{3}{4}$.

Step10: Solve 17) $\tan A$

For the right - triangle with sides 20, 21, and 29, the side opposite to $\angle A$ is 21 and the side adjacent to $\angle A$ is 20. So, $\tan A=\frac{21}{20}$.

Step11: Solve 18) $\sin C$

For the right - triangle with sides 20, 21, and 29, the side opposite to $\angle C$ is 20 and the hypotenuse is 29. So, $\sin C=\frac{20}{29}$.

Step12: Solve 19) $\cos C$

For the right - triangle with sides 30, 40, and 50, the side adjacent to $\angle C$ is 40 and the hypotenuse is 50. So, $\cos C=\frac{40}{50}=\frac{4}{5}$.

Step13: Solve 20) $\cos X$

For the right - triangle with sides 14, 48, and 50, the side adjacent to $\angle X$ is 48 and the hypotenuse is 50. So, $\cos X=\frac{48}{50}=\frac{24}{25}$.

Answer:

1. $\frac{5}{13}$
2. $\frac{4}{5}$
3. $\frac{35}{37}$
4. $\frac{5}{12}$
5. $\frac{3}{5}$
6. $\frac{3}{4}$
7. $\frac{5}{13}$
8. $\frac{3}{4}$
9. $\frac{21}{20}$
10. $\frac{20}{29}$
11. $\frac{4}{5}$
12. $\frac{24}{25}$