balloon problem
tan (theta) = ( h - 48.2) / x
tan 14.7 = (61.5 - 48.2)/x
x = 50.7 m
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as per law of cosine
cos (alpha) = ( b^2 + c^2 - a^2)/ ( 2 b*c)
cos alpha = ( 145^2 + 172^2 - 90^2) /( 2 * 145* 172)
alpha = 31.545
Similarly
cos (beta) = ( a^2 + c^2 - b^2)/( 2 a c)
cos (beta) = ( 90^2 + 172^2 - 145^2) / (2* 90*172)
beta = 57.44
again
cos( gamma) = ( a^2 + b^2 - c^2) / ( 2 ab)
cos ( gamma) = ( 90^2 + 145^2 - 172^2) / ( 2* 90* 145)
gamma = 91.015
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Do comment in case any doubt, will reply for sure.. Goodluck
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