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

1 Answer
Noah G
Nov 26, 2016

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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