How do you solve the triangle ABC, given a=22, A=50, c=27?

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How do you solve the triangle ABC, given a=22, A=50, c=27?

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Answer 1 · 2018-02-25T08:26:16

To 'solve' a triangle means to find all the missing values for the sides and angles. In this case, the lengths of $2$ $2$ sides and the size of $1$ $1$ angle are given, we have to find the size of the $3 r d$ $3 rd$ side and the other $2$ $2$ angles.

$ˆ C = 70, ˆ B = 60, b = 24.87$ $color(green)(hat C = 70, hat B = 60, b = 24.87$

Explanation:

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$sin C = \frac{c sin A}{a} = \frac{27 sin 50}{22} = 0.9401$ $sin C = (c sin A) / a = (27 sin 50) / 22 = 0.9401$

$ˆ C = {sin}^{- 1} 0.9401 = 70^{\circ}$ $hat C = sin ^-1 0.9401 = 70^@$

$ˆ B = 180 - 50 - 70 = 60^{\circ}$ $hat B = 180 - 50 - 70 = 60^@$

$b = \frac{a \cdot sin B}{sin A} = \frac{22 \cdot sin 60}{sin 50} = 24.87$ $b = (a * sin B) / sin A = (22 * sin 60) / sin 50 = 24.87$

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How do you solve the triangle ABC, given a=22, A=50, c=27?

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