Question

Someone please help me, i’ve been struggling.

Answer 1

Triangle a: 44.7°

Triangle b: 30.5°

Triangle c: 67.4°

Triangle d: 56.6°

Explanation:

Recall: SOHCAHTOA

a. Reference angle =
`\theta`

Opposite = 19

Hypotenuse = 27

Apply SOH:

`sin(\theta) = (Opp)/(Hyp)`

`sin(\theta) = (19)/(27)`

`\theta = sin^(-1)((19)/(27))`

`\theta = 44.7 degrees` (nearest tenth)

b. Reference angle =
`\theta`

Opposite = 33

Adjacent = 56

Apply TOA:

`tan(\theta) = (Opp)/(Adj)`

`tan(\theta) = (33)/(56)`

`\theta = tan^(-1)((33)/(56))`

`\theta = 30.5 degrees` (nearest tenth)

c. Reference angle =
`\theta`

Opposite = 12

Adjacent = 5

Apply TOA:

`tan(\theta) = (Opp)/(Adj)`

`tan(\theta) = (12)/(5)`

`\theta = tan^(-1)((12)/(5))`

`\theta = 67.4 degrees` (nearest tenth)

d. Reference angle =
`\theta`

Hypotenuse = 20

Adjacent = 11

Apply CAH:

`cos(\theta) = (Adj)/(Hyp)`

`cos(\theta) = (11)/(20)`

`\theta = cos^(-1)((11)/(20))`

`\theta = 56.6 degrees` (nearest tenth)