Question

Use the diagram to express each ratio as a fraction.

Answer 1

Answer/Step-by-step explanation:

Recall the acronym for trigonometric ratios: SOHCAHTOA

SOH means sine of the reference angle = opp/hypotenuse

CAH means cosine of the reference angle = Adj/hyp

TOA means tangent of the reference angle = opp/adj

a. Reference angle = A

opp = 15

hypotenuse = 17

Therefore:

`sin(A) = (opp)/(hypo) = (15)/(17)`

b. Reference angle = A

`cos(A) = (adj)/(hypo)`

Adj = 8

hypotenuse = 17

Therefore:

`cos(A) = (8)/(17)`

c. Reference angle = A

`tan(A) = (opp)/(adj)`

Adj = 8

Opp = 15

Therefore:

`tan(A) = (15)/(8)`

d. Reference angle = B

`sin(B) = (opp)/(hypo)`

Opp = 8

hypotenuse = 17

Therefore:

`sin(B) = (8)/(17)`

e. Reference angle = B

`cos(B) = (adj)/(hypo)`

Adj = 15

hypotenuse = 17

Therefore:

`cos(B) = (15)/(17)`

d. Reference angle = B

`tan(B) = (opp)/(adj)`

Opp = 8

Adj = 15

Therefore:

`tan(B) = (8)/(15)`