Question

Law of sines: In △BCD, d = 3, b = 5, and m∠D = 25°. What are the possible approximate measures of angle B?

only 90°

only 155°

20° and 110°

45° and 135°

Answer 1

45° and 135°

Explanation:

The law of sines states

`(\sin A)/(a)=(\sin B)/(b)=(\sin C)/(c)`

Using the information we have,

`(\sin 25)/(3)=(\sin B)/(5)`

Cross multiplying, we have

`5\sin 25=3\sin B`

Divide both sides by 3:

`(5\sin 25)/(3)=\sin B`

To cancel the sine function, apply the inverse sine:

`\sin^(-1)((5\sin 25)/(3))=B\\\\44.78 \approx B`

This means B can be either 45° or 135°.

Answer 2

≈Law of sines:

b d
------- = ----------
sin(B) sin(D)

=> sin(B) = sin(D) * b / d

sin(B) = sin(25°) * 5 / 3 ≈ 0.4226 * 5/3 = 0.7043

=> B = arcsine(0.7043) ≈ 45° or 135°

Answer: 45° and 135°