How do you find the height of a scalene triangle when given 2 angles and 1 side: side c = 1200, Angle A = 72, Angle B = 77?

1 Answer
sankarankalyanam
Oct 22, 2017

Height #h_c = 2159.1276 color (white)(aaa) #where #h_c #is height of the triangle with base c = 1200#

Explanation:

Three angles are #72^0, 77^0 & 31^0#
# a / sin A = b / sin B = c / sin C#

# a / sin 72 = b / sin 77 = 1200 / sin 31#

#:. a = (1200* sin 72) / sin 31 = 2215.8902#

# b = (1200 * sin 77) / sin 31 = 2270.209#

Semi perimeter# s = ( a + b + c)/2 = 5686.0991/2 = 2843.0496#
#s - a = 2843.0496-2215.8902 = 627.1594#
#s - b = 2843.0496 - 2270.209 = 572.8406#
#s - c = 2843.0496 - 1200 = 1643.0496#

Area of #Delta = sqrt(s (s-a) ( s - b) (s - c)) #

#Area = sqrt(2843.0496*627.1594*572.8406*1643.0496)#
#Area = 1295476.5347#

But #Area = (1/2) * c * h _c = (1/2) * 1200 * h_c# where c is the base.
#:. h_c = (1295476.5347* 2) / 1200 = 2159.1276#

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