Law of sines: In △BCD, d = 3, b = 5, and m∠D = 25°. What are the possible approximate measures of angle B? only 90° <

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°

0

Answers ( No )

    0
    2021-11-23T20:21:46+00:00

    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°.

    0
    2021-11-23T20:22:18+00:00

    ≈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°

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