Question

I need to find the measure of each angle indicated

Answer 1

1. From the given right-triangle, the side opposite to $\theta$ is 6.8 units.

The adjacent side to $\theta$ is 4 units.

Recall the mnemonics, SOH-CAH-TOA.

We use the tangent ratio to obtain:

$\tan \theta=\frac{Opposite}{Adjacent}$

$\tan \theta=\frac{4}{6.8}$

$\tan \theta=\frac{10}{17}$

$\implies \theta=\tan^{-1}(\frac{10}{17})$

$\implies \theta=30.5\degree$ to the nearest tenth.

2. This time we were given the hypotenuse to be 15.7 units and the adjacent side is 6 units.

We use the cosine ratio to obtain:

$\cos \theta=\frac{Adjacent}{Hypotenuse}$

$\cos \theta=\frac{6}{15.7}$

$\cos \theta=\frac{60}{157}$

$\implies \theta=\cos^{-1}(\frac{60}{157})$

$\implies \theta=67.5\degree$ to the nearest tenth.

Answer 2

Answer:

25).  55.02°

26).  30.46°

Step-by-step explanation:

Points to remember

Trigonometric ratios

Sin θ  = Opposite side/Hypotenuse

Cos θ = Adjacent side/Hypotenuse

Tan θ = Opposite side/Adjacent side

To find the answer of question 25

Cos θ = Adjacent side/Hypotenuse

 = 9/15.7 = 0.573

θ = Cos⁻¹(0.573) = 55.02°

To find the answer of question 26

Tan θ = Opposite side/Adjacent side

 = 4/6.8 = 0.588

θ = Tan⁻¹(0.588) = 30.46°