How do you solve the triangle ABC, given a=40, A=25, c=30?

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How do you solve the triangle ABC, given a=40, A=25, c=30?

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Answer 1 · 2017-07-08T20:12:30

$hatC = 18.5°," "hatB = 136.5° " and side " b = 65.2$

Explanation:

Angle A and side 'a' form a complete matching pair, so we can use the Sine rule to find angle C.
Angle A is opposite side 'a' and angle C is opposite side 'c'.

$(sin C)/c = (sin A)/a$

$(sin C)/30 = (sin 25)/40$

$sin C = (30sin25)/40 = 0.31696$

$hatC = 18.5°$

Now that we have two of the angles we can find the third angle from the sum of the angles in a triangle:

$hatB = 180°-25°-18.5° = 136.5°$

Use the Sine rule to find the length of side 'b'.

$b/(sin B) = a/(sin A)$

$b = (40sin136.5)/(sin25)$

$b= 65.2$

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How do you solve the triangle ABC, given a=40, A=25, c=30?

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