In the pictured triangle, 2A is 98 degrees and 2B is 12 degrees. If side a is 84 units long, approximately how long is side b?<

Question

In the pictured triangle, 2A is 98 degrees and 2B is 12 degrees. If side a is 84
units long, approximately how long is side b?

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Autumn 2 weeks 2021-09-09T06:56:22+00:00 1 Answer 0

Answers ( )

    0
    2021-09-09T06:58:20+00:00

    The length of the side b is 17.82 units

    Explanation:

    Given that the triangle has ∠A = 98° and ∠B = 12°

    Also, given that the side a has length a = 84 units

    We need to determine the length of the side b

    To determine the length of the side b, we shall use the law of sine formula.

    The law of sine formula is given by

    \frac{sin \ A}{a} = \frac{sin \ B}{b}

    Substituting the values in the above formula,we have,

    \frac{sin \ 98^{\circ}}{84} = \frac{sin \ 12^{\circ}}{b}

    Simplifying, we get,

    \frac{0.99}{84} = \frac{0.21}{b}

    Cross multiplying, we get,

    0.99\times b=0.21\times 84

    Multiplying, we get,

    0.99b=17.64

    Dividing both sides by 0.99, we get,

    b=17.82

    Thus, the length of the side b is approximately 17.82 units.

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