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

≈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°

Answer 2

Answer:

45° and 135°

Step-by-step explanation:

The law of sines states

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

Using the information we have,

$\frac{\sin 25}{3}=\frac{\sin B}{5}$

Cross multiplying, we have

$5\sin 25=3\sin B$

Divide both sides by 3:

$\frac{5\sin 25}{3}=\sin B$

To cancel the sine function, apply the inverse sine:

$\sin^{-1}(\frac{5\sin 25}{3})=B\\\\44.78 \approx B$

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