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The Sine and Cosine Rules - Example 2

Here we are given two sides and the angle included between them.

Ex1Tri.GIF - 3836 bytes

First we use the Cosine Rule to find a.

NTEX2calc1.GIF - 4Kb

Your calculator says 82.92812421 and this is stored in ANS but you will write down 83mm.

Now we find the smaller of the two remaining angles, we know this must be acute.

As c is the smallest side C is the smallest angle.

NTEx2B1 - 1451 bytes

Your calculator says 45.71217982 and this is stored in ANS but you will write down 46°.

Quick sum in your head: 46 + 58 > 90 so B is also acute.

NTex2B2 - 1447 bytes

So B = sin-1ANS Your calculator says 76.28782018 but you will write down 76°

So a = 83 mm, B = 76° and C = 46°

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© Barry Gray April 2016