Trigonometry · Ordinary Level
Sine Rule — Finding an Angle
Ordinary Level · Class 7 · Tap NEXT to begin
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The Sine Rule — Finding an Angle
Flip it over
To find an angle, turn the rule upside-down so the angles are on top: $\dfrac{\sin A}{a} = \dfrac{\sin B}{b}$. Then use $\sin^{-1}$.
Worked example — find angle A
In a triangle $a = 15$, $b = 19$ and $B = 51^\circ$. Find $A$.
$\dfrac{\sin A}{15} = \dfrac{\sin 51}{19}$
$\sin A = \dfrac{15\sin 51}{19} = 0.61 \Rightarrow A = 37.84 = 38^\circ$
$A = 38^\circ$
Worked example — with a 90+ angle known
In a triangle $a = 12$, $b = 21$ and $B = 130^\circ$. Find $A$.
$\dfrac{\sin A}{12} = \dfrac{\sin 130}{21}$
$\sin A = \dfrac{12\sin 130}{21} = 0.4 \Rightarrow A = 25.95 = 26^\circ$
$A = 26^\circ$
Worked example — another pair
In a triangle $a = 9$, $b = 7$ and $B = 47^\circ$. Find $A$.
$\sin A = \dfrac{9\sin 47}{7} = 0.9 \Rightarrow A = 70^\circ$
$A = 70^\circ$
You try
In a triangle $a = 9$, $b = 8$ and $B = 61^\circ$. Find $A$.
$\sin A = \dfrac{9\sin 61}{8}$.
$\sin A = 0.98 \Rightarrow A = 79.7 = 80^\circ$
$A = 80^\circ$
You try
In a triangle $a = 9$, $b = 8$ and $B = 30^\circ$. Find $A$.
$\sin A = \dfrac{9\sin 30}{8}$.
$\sin A = 0.5625 \Rightarrow A = 34^\circ$
$A = 34^\circ$
You try
In a triangle $a = 12$, $b = 15$ and $B = 37^\circ$. Find $A$.
$\sin A = \dfrac{12\sin 37}{15}$.
$\sin A = 0.4 \Rightarrow A = 28.7 = 29^\circ$
$A = 29^\circ$
You try
A triangle has a side $8$ facing $56^\circ$, and a side $9$ facing angle $A$. Find $A$.
$\dfrac{\sin A}{9} = \dfrac{\sin 56}{8}$.
$\sin A = \dfrac{9\sin 56}{8} = 0.93 \Rightarrow A = 68.8 = 69^\circ$
$A = 69^\circ$
That’s Class 7.
Flip the Sine Rule to find an angle. Class 8: the Cosine Rule for a side.