MATH 1113 PreCalculus

Day #33, Law of Cosines, II

The final situation: Side-Side-Side

Given any three sticks, of lengths a, b, and c, there is always a unique triangle that can be formed from them, PROVIDED THAT every side is shorter than the sum of the other two sides (think about it.)

Here's a Geogebra applet that lets you play with three sticks.

Applet

Here's an example of solving a triangle using "Side-Side-Side"

Applet

Example: Solve the triangle with sides of length:  3.43, 6.39, and 8.17.

Solution: First note that 8.17 < (3.43 + 6.39), so there IS a triangle (see the picture, above.)

First, use the Law of Cosines to find the largest angle (the one opposite side length 8.17.)

Angle B = ArcCos((3.43² + 6.39² - 8.17²)/(2*3.43*6.39))

              = ArcCos( -0.32284) = 108.83^o (notice that the applet is slightly off.)

Notice that, since this is an obtuse angle, it could not have been found using the Law of Sines.  That's why we find the largest angle first.

Now, use the Law of sines to find either other angle:

Angle A = ArcSin(6.39*sin(108.83)/8.17) = 47.75^o

Then find the third angle by subtraction:

Angle C = 180 - (47.75 + 108.83) = 23.42^o

Page Last Modified: 28 March, 2007

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