Answer:
5. m<A = 25.3°; m<B = 64.7°
6. m<A = 40.2°; m<B = 49.8°
Explanation:
Recall: SOHCAHTOA
5. Reference angle = <A
Opposite = 9
Adjacent = 19
Apply TOA:
Tan A = Opp/Adj
Tan A = 9/19
A = Tan^{-1}(9/19)
A = 25.3461759° ≈ 25.3° (nearest tenth)
Reference angle = <B
Opposite = 19
Adjacent = 9
Apply TOA:
Tan B = Opp/Adj
Tan B = 19/9
B = Tan^{-1}(19/9)
B = 64.6538241° ≈ 64.7° (nearest tenth)
6. Reference angle = A
Opposite = 20
Hypotenuse = 31
Apply SOH:
Sin A = Opp/Hyp
Sin A = 20/31
A = sin^{-1}(20/31)
A = 40.2° (nearest tenth)
Reference angle = B
Adjacent = 20
Hypotenuse = 31
Apply CAH:
Cos B = Adj/Hyp
Cos B = 20/31
B = cos^{-1}(20/31)
B = 49.8° (nearest tenth)