How do you find the length of a triangle's sides using only its angles: 35, 65, 80 and the area is 4000?

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How do you find the length of a triangle's sides using only its angles: 35, 65, 80 and the area is 4000?

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Answer 1 · 2016-11-26T02:43:01

In $DeltaABC$ , the area is given by $A = 1/2ab sin C$ . We let the sides be $a$ , $b$ and $c$ . Hence, we write a system of equations in three variables to describe the situation.

$4000 = 1/2ab sin(35)$

$4000 = 1/2bc sin(65)$

$4000 = 1/2ac sin(80)$

We use a graphing calculator or C.A.S (Computer Algebra System) to solve.

We get: $a ~= 113.295$ , $b~= 123.108$ and $c~= 71.7013$

Hopefully this helps!

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How do you find the length of a triangle's sides using only its angles: 35, 65, 80 and the area is 4000?

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