In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest tenth. 2) c= 16, b=14​

Question

In each problem, angle C is a right angle. Solve each triangle rounding answers to the nearest
tenth.
2) c= 16, b=14​

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Khải Quang 4 years 2021-08-24T12:36:39+00:00 1 Answers 4 views 0

Answers ( )

  1. trungdung22
    0
    2021-08-24T12:38:24+00:00
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    Answer:

    B = 61°

    A = 29°

    a = 10

    Step-by-step explanation:

    We are given;

    c = 16, b = 14​

    Since we are told that C is a right angle, it means that C = 90°

    Thus using sine rule, we have;

    c/sin C = b/sin B

    16/sin 90 = 14/sin B

    16/1 = 14/sin B

    sin B = 14/16

    sin B = 0.875

    B = sin^(-1) 0.875

    B ≈ 61°

    Now, since C is a right angle, it means that c will be the hypotenuse of the triangle.

    Thus, from pythagoras theorem, If the other side of the triangle is a, then;

    a² + b² = c²

    a² + 14² = 16²

    a² = 16² – 14²

    a² = 256 – 156

    a² = 100

    a = √100

    a = 10

    Since we know B and C, we can find A because sum of angles in a triangle is 180°.

    Thus;

    A = 180 – (B + C)

    A = 180 – (61 + 90)

    A = 29°

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