Answer:
74.3 and 105.7
Step-by-step explanation:
In ΔUVW, v = 39 inches, u = 37 inches and ∠U=66°. Find all possible values of ∠V, to the nearest 10th of a degree.
U
V
W
u = 37
v = 39
66°
?°
\frac{\sin A}{a}=\frac{\sin B}{b}
a
sinA
=
b
sinB
From the reference sheet (reciprocal version).
\frac{\sin V}{39}=\frac{\sin 66}{37}
39
sinV
=
37
sin66
Plug in values.
\sin V=\frac{39\sin 66}{37}\approx 0.9629263
sinV=
37
39sin66
≈0.9629263
Evaluate.
V=\sin^{-1}(0.9629263)\approx 74.35\approx 74.3^{\circ}
V=sin
−1
(0.9629263)≈74.35≈74.3
∘
Inverse sine and round.
\text{Quadrant II: } 180-74.3=105.7^{\circ}
Quadrant II: 180−74.3=105.7
∘
Sine is positive in quadrants 1 and 2.
\text{Check for possibility:}
Check for possibility:
No triangle's angles may add to more than 180.
66+74.3=140.3^{\circ}\leftarrow \text{Possible}
66+74.3=140.3
∘
←Possible
Less than 180.
66+105.7=171.7^{\circ}\leftarrow \text{Possible}
66+105.7=171.7
∘
←Possible
Less than 180.
\text{Answer: }74.3^{\circ}\text{ and } 105.7^{\circ}
Answer: 74.3
∘
and 105.7
∘
