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?

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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?

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Answer 1 · 2017-10-22T03:54:32

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

Explanation:

Three angles are $72^{0}, 77^{0} & 31^{0}$ $72^0, 77^0 & 31^0$
$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a / sin A = b / sin B = c / sin C$

$\frac{a}{sin 72} = \frac{b}{sin 77} = \frac{1200}{sin 31}$ $a / sin 72 = b / sin 77 = 1200 / sin 31$

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

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

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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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?

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