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What is the measure of

What is the measure of-example-1
User Michaelmeyer
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1 Answer

26 votes
26 votes

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)

User Beebul
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