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Hoochie [10]
2 years ago
13

Vertices A and B of triangle ABC are on one bank of a river, and vertex C is on the opposite bank. The distance between A and B

is 200 feet. Angle A has a measure of 33°, and angle B has a measure of 63°. Find b. 110 ft
168 ft
179 ft
223 ft

Mathematics
1 answer:
Anna71 [15]2 years ago
7 0

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,

\frac{\sin \angle A}{a}=\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}

\frac{\sin \angle B}{b}=\frac{\sin \angle C}{c}

\frac{\sin 63^{\circ}}{b}=\frac{\sin 84^{\circ}}{200}

b=200\times \frac{\sin 63^{\circ}}{\sin 84^{\circ}}=179.182887\sim 179 ft

The length of side b is 179 ft

Option C is correct.

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