How do you use the sine rule to find an angle?

Answer 1

The Sine Rule is

SinA/a = SinB /b = SinC/c

For any given triangle, where two sides and one angle are known, use the Sine Rule

If the two sides are 'a' & 'b' , and Angle 'B' is known then, initially ignore the C/c compoentne.

So it reduces to

SinA/a = SinB/b

To find SinA

Then

SinA = aSinB/b

For example if Angle B = 30 degrees , 'a' = 3 & 'b' = 5

Then substituting

SinA = 3Sin30/ 5

First find the Sine of 30 , which is 0.5

Hence

SinA = 3*0.5/5

SinA = 1.5/5

SinA = 0.3

Hence

A = Sin^(-1) 0.3 (or ArcSin(0.3)) = 17.457.... degrees.

NB Select any two terms from 'A/a' B/b , or C/c'. Do NOT try to use all three in one calculation.

NNB Sometimes the Sine Rule is written as

a/SinA = b/SinB = c/SinC

However, it works just the same.

Hope that helps!!!!!

Answer 2

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