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4.03 The sine rule

Interactive practice questions

We want to prove the sine rule: $\frac{\sin A}{a}=\frac{\sin B}{b}$sinAa=sinBb

a

Consider the $\triangle ACD$ACD, find an expression for $\sin A$sinA.

b

Consider $\triangle BDC$BDC, find an expression for $\sin B$sinB.

c

Make $x$x the subject of the equation $\sin B=\frac{x}{a}$sinB=xa.

d

Substitute $x=a\sin B$x=asinB into $\sin A=\frac{x}{b}$sinA=xb and prove the Sine Rule.

e

True or false:

$\frac{\sin A}{a}$sinAa=$\frac{\sin B}{b}$sinBb=$\frac{\sin C}{c}$sinCc

True

A

False

B
Medium
3min

Consider a triangle where all three sides are known, but no angles are known. Is there enough information to find all the angles in the triangle using only the sine rule?

Easy
< 1min

Consider a triangle where two of the angles and the side included between them are known. Is there enough information to solve for the remaining sides and angle using just the sine rule?

Easy
< 1min

Consider a triangle where two of the sides and an angle included between them are known. Is there enough information to solve for the remaining side and angles using just the sine rule?

Easy
< 1min
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Outcomes

1.2.4

establish and use the sine and cosine rules, including consideration of the ambiguous case and the formula Area=1/2 bc sin⁡A for the area of a triangle

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