Question

What is the measure of

Answer 1

Answer: D

Explanation:

By the cosine rule,
`BC=\sqrt{10^(2)+14^(2)-2 \cdot 10 \cdot 14 \cdot \cos 70^(\circ)}`

Now, we can use the law of sines to get that:

`\frac{\sqrt{10^(2)+14^(2)-2\cdot 10 \cdot 14 \cdot \cos 70^(\circ)}}{\sin 70^(\circ)}=(14)/(\sin \angle ABC)`

Meaning that
`\sin \angle ABC =\frac{14\sin 70^(\circ)}{\sqrt{10^(2)+14^(2)-2 \cdot 10 \cdot 14 \cdot \cos 70^(\circ)}}`

And thus
`\angle ABC=\sin^(-1) \left(\frac{14\sin 70^(\circ)}{\sqrt{10^(2)+14^(2)-2 \cdot 10 \cdot 14 \cdot \cos 70^(\circ)}} \right) \approx 68.39^(\circ)`