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Expert: - 8/11/2011


Question
Triangle
Triangle
How do i find the side lengths of this triangle? (in image below). I do not need to know the side lengths x and y separately, but just the sum of x+y. The area of the triangle on the right is 10,000 meters^2, with one of the side lengths 85 meters, and one of the angles 120.2 degrees.

Answer
I think you can start by using these ideas:
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Draw AD perpendicular to AB, extended.  It falls to the left of B.

AD can be determined by AD = 125 sin 36

= 73.5
.........................
x and y are related by the law of cosines:

x^2 = 85^2 + y^2 - 2y(85) cos 120.2
............................
AD can also be written:

AD = x sin C  (we don't know x or C, yet)
.........................
the area of triangle ABC is:

ABC = 1/2 x y sin C

But x sin C = AD = 73.5, so:

ABC = 1/2 y (73.5) and

10000 = 1/2 y (73.5)

So you can now compute y.  With that, you can use the Law of cosines above to find x.

That should do it.

Paul Klarreich

Expertise

I can answer questions in basic to advanced algebra (theory of equations, complex numbers), precalculus (functions, graphs, exponential, logarithmic, and trigonometric functions and identities), basic probability, and finite mathematics, including mathematical induction. I can also try (but not guarantee) to answer questions on Abstract Algebra -- groups, rings, etc. and Analysis -- sequences, limits, continuity. I won't understand specialized engineering or business jargon.

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I taught at a two-year college for 25 years, including all subjects from algebra to third-semester calculus.

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