Question

I need to find the measure of each angle indicated please help

Answer 1

We shall use the mnemonics SOH-CAH-TOA to find the missing angles.

SOH- means sine ratio is $\frac{Opposite}{Hypotenuse}$

CAH- means cosine ratio is $\frac{Adjacent}{Hypotenuse}$

TOA- means tangent ratio is $\frac{Opposite}{Adjacent}$

11) From the given right-angle triangle,the side length adjacent to $\theta$ is 11 units.

The opposite side  is 8 units.

We use the tangent ratio to obtain:

$\tan \theta=\frac{8}{11}$

$\theta=\tan ^{-1}(\frac{8}{11})$

$\theta=36.0\degree$ to the nearest tenth.

12) From the given right-angle triangle,the side length adjacent to $\theta$ is 7 units.

The opposite side  is 13 units.

We use the tangent ratio to obtain:

$\tan \theta=\frac{13}{7}$

$\theta=\tan ^{-1}(\frac{13}{7})$

$\theta=61.7\degree$ to the nearest tenth.

13) From the given right-angle triangle,the side length adjacent to $\theta$ is 8 units.

The opposite side  is 11 units.

We use the tangent ratio to obtain:

$\tan \theta=\frac{11}{8}$

$\theta=\tan ^{-1}(\frac{11}{8})$

$\theta=54.0\degree$ to the nearest tenth.

14. This time we were given the hypotenuse to be 9.7 units and the opposite side of the right-angle triangle is 7 units.

We use the sine ratio to obtain:

$\sin \theta=\frac{7}{9.7}$

$\implies \sin \theta=\frac{70}{97}$

$\implies \sin \theta=\frac{70}{97}$

$\implies \theta=\sin^{-1}(\frac{70}{97})$

$\implies \theta=46.2\degree$

15. For question 15; we the hypotenuse to be 7 units and the adjacent side is 4 units.

We use the cosine ratio to get;

$\cos \theta=\frac{4}{7}$

$\implies \theta=\cos^{-1}(\frac{4}{7})$

$\implies \theta=55.2\degree$ to the nearest tenth.

16) From the given right-angle triangle,the side length adjacent to $\theta$ is 13 units.

The opposite side  is 12 units.

We use the tangent ratio to obtain:

$\tan \theta=\frac{12}{13}$

$\theta=\tan ^{-1}(\frac{12}{13})$

$\theta=42.7\degree$ to the nearest tenth.