Answer:
The length of side b is 179 ft
Step-by-step explanation:
Given triangle ABC in which
∠A = 33°, ∠B = 63°, c=200
we have to find the length of b
In ΔABC, by angle sum property of triangle
∠A+∠B+∠C=180°
33°+63°+∠C=180°
∠C=180°-33°-63°=84°
By sine law,
[tex]\frac{\sin \angle A}{a}=\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}[/tex]
[tex]\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}[/tex]
[tex]\frac{\sin 63^{\circ}}{b}=\frac{\sin 84^{\circ}}{200}[/tex]
[tex]b=200\times \frac{\sin 63^{\circ}}{\sin 84^{\circ}}=179.182887\sim 179 ft[/tex]
The length of side b is 179 ft
Option C is correct.
