Question

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?

Answer 1

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`