In ΔSTU, s = 580 inches, u = 440 inches and ∠U=17°. Find all possible values of ∠S, to the nearest 10th of a degree. S
T
U
s = 580
u = 440
?°
17°
\frac{\sin A}{a}=\frac{\sin B}{b}
a
sinA
​
=
b
sinB
​

From the reference sheet (reciprocal version).
\frac{\sin S}{580}=\frac{\sin 17}{440}
580
sinS
​
=
440
sin17
​

Plug in values.
\sin S=\frac{580\sin 17}{440}\approx 0.3853991
sinS=
440
580sin17
​
≈0.3853991
Evaluate.
S=\sin^{-1}(0.3853991)\approx 22.669\approx 22.7^{\circ}
S=sin
−1
(0.3853991)≈22.669≈22.7
∘

Inverse sine and round.
\text{Quadrant II: } 180-22.7=157.3^{\circ}
Quadrant II: 180−22.7=157.3
∘

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.
17+22.7=39.7^{\circ}\leftarrow \text{Possible}
17+22.7=39.7
∘
←Possible
Less than 180.
17+157.3=174.3^{\circ}\leftarrow \text{Possible}
17+157.3=174.3
∘
←Possible
Less than 180.
\text{ }22.7^{\circ}\text{ and } 157.3^{\circ}
22.7
∘
and 157.3
∘