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