In each set, one thing changes and everything else stays the same. Work them out in order and look for the pattern — the last line tells you what to notice.
①Sine rule: only angle $B$ changeschanging: angle $B$
Find side $b$ to 1 d.p. Here $A=40^\circ$ and $a=8$ cm each time.
$B=60^\circ$
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$B=75^\circ$
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$B=90^\circ$
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As angle $B$ grows, its opposite side $b$ grows too. What happens as $B$ approaches $90^\circ$?
②Cosine rule: only the included angle changeschanging: the included angle $A$
Find side $a$ to 1 d.p. Here $b=8$ cm and $c=6$ cm each time.
$A=40^\circ$
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$A=60^\circ$
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$A=90^\circ$
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At $A=90^\circ$ the cosine rule becomes Pythagoras ($\cos90^\circ=0$). Check that answer!
③Area: only the included angle changeschanging: the included angle $C$
Find the area to 1 d.p. The two sides are $9$ cm and $7$ cm each time.
$C=25^\circ$
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$C=50^\circ$
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$C=90^\circ$
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The area is largest when the included angle is $90^\circ$. Why?
Answers · Sine & Cosine Rule
Variation practice
① Sine rule: only angle $B$ changes
$B=60^\circ$: 10.8 cm$B=75^\circ$: 12.0 cm$B=90^\circ$: 12.4 cm
② Cosine rule: only the included angle changes
$A=40^\circ$: 5.1 cm$A=60^\circ$: 7.2 cm$A=90^\circ$: 10.0 cm
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