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.
2 answers:
A suitable solver will tell you instantly that the measure of b is 179.18 ft.
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If you want to do it yourself (meaning also with the aid of a calculator), you can use the Law of Sines. The given side is side "c", so you need the measure of angle C. That will be
180° -33° -63° = 84°
Then side "b" can be found from
b/sin(B) = c/sin(C)
b = c*sin(B)/sin(C)
b = (200 ft)*sin(63°)/sin(84°) ≈ 179.183 ft
_____
If you want to do it yourself (meaning also with the aid of a calculator), you can use the Law of Sines. The given side is side "c", so you need the measure of angle C. That will be
180° -33° -63° = 84°
Then side "b" can be found from
b/sin(B) = c/sin(C)
b = c*sin(B)/sin(C)
b = (200 ft)*sin(63°)/sin(84°) ≈ 179.183 ft
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