Find $\angle ABC$

Geometry Level 2

In $\triangle ABC$ , $\overline{AB} = 3 , \overline{BC} = 2$ and $\angle ACB = 110^{\circ}$ . Find $\angle ABC$ in degrees.

The answer is 31.21.

1 solution

Toby M
Dec 6, 2020

Sine rule gives $\frac{\sin \angle BAC}{2} = \frac{\sin 110º}{3} \Rightarrow \angle BAC = \arcsin \frac{2 \sin 110º}{3} \approx 38.79º$ . Therefore $\angle ABC = 180º - 110º - \angle BAC \approx 31.21º$ .

Find ∠ A B C \angle ABC ∠ A B C

The answer is 31.21.

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Find $\angle ABC$