How do you determine the number of possible triangles and find the measure of the three angles given $a=8, b=10, mangleA=45$ ?

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Answer 1 · 2018-02-26T06:24:27

Solution (1) $hat. = 45^@, hat B = 62.12^@, hat C = 72.88^@$

Solution (2) $hat. = 45^@, hat B = 117.88^@, hat C = 17.12^@$

$hat A = 45, a = 8, b = 10$

Applying law of sines,

$sin B = (sin A * b) / a = (sin 45 * 10) / 8 ~~ 0.8839$

$hat B = sin ^-1 0.8839 ~~ 62.12$

$hat C = 180 - 45 - 62.12 = 72.88^@$

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Since $hat A + hatB = 45 + 62.12 = 107.12$ is less than $180^@$ , we will have one more solution.

Supplementary angle of $hat B = 180 - 62.12 = 117.88^@$

$hat C = 180 - 117.88 - 45 = 17.12^@$

enter image source here

How do you determine the number of possible triangles and find the measure of the three angles given a=8, b=10, mangleA=45a=8, b=10, mangleA=45?