in the following triangle, theta= 60. find the values of the angles B and B', which solve this ambiguous case

∠B + ∠B= 180° The Sine Law: 10 / sin B = 9.2 / sin 60°
10 / sin B= 9.2 / √3/2 sin B = 0.94133
B= sin^(-1) 0.94133 Answer: C ) ∠B = 109.73°, ∠B = 70.27°

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Lanuel Lanuel · Answer 2 · 2022-07-08T20:43:29-04:00

By apply the law of sine, the magnitude of both angles B and B', which solve this ambiguous case are 64.13° and 115.87° respectively.

How to determine angles B and B'?

In order to determine the magnitude of both angles B and B', we would apply the law of sine:

\(\frac{sinA}{a} =\frac{sinB}{b} =\frac{sinC}{c}\)

Substituting the parameters into the formula above, we have;

sinB'/16 = sin60/15.4

sinB'/16 = 0.8660/15.4

sinB'/16 = 0.0562

sinB' = 0.0562 × 16

B' = sin⁻¹(0.8992)

B' = 115.87°.

Now, we can determine the magnitude of angle B by using the formula for supplementary angles:

B + B' = 180

B + 115.87 = 180

B = 180 - 115.87

B = 64.13°.

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