Question

I need to find the measure of each angle indicated

Answer 1

25). 55.02°

26). 30.46°

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°

Answer 2

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=(Opposite)/(Adjacent)`

`\tan \theta=(4)/(6.8)`

`\tan \theta=(10)/(17)`

`\implies \theta=\tan^(-1)((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=(Adjacent)/(Hypotenuse)`

`\cos \theta=(6)/(15.7)`

`\cos \theta=(60)/(157)`

`\implies \theta=\cos^(-1)((60)/(157))`

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