Question

In the following triangle theta=60.Find the values of the angles of the angles B and B'

lengths of sides are 15.4 on the first two and 16 on the third side

Answer 1

∠B` = 109.73°, ∠B = 70.27°

Explanation:

∠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

∠B` = 109.73°, ∠B = 70.27°

Answer 2

By applying the law of sine, the magnitude of both angles B and B', which solve this ambiguous case include; A. B = 64.13⁰ or B' = 115.87⁰

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

`(sinA)/(a) =(sinB)/(b) =(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°.

Complete Question:

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