Question

Use Law of Sines to solve for the length for sides AB and AC. Round your answer to the nearest TENTH.

Answer 1

First, we calculate the measure of angle A. We know that the sum of the internal angles of a triangle is 180°. Then:

`\begin{gathered} 45°+70°+\angle A=180° \\ 115\degree+\angle A=180\degree \\ \\ \Rightarrow\angle A=65\degree \end{gathered}`

Finally, using the law of Sines:

`\begin{gathered} (BC)/(\sin A)=(AC)/(\sin B)=(AB)/(\sin C) \\ \\ \Rightarrow(BC)/(\sin65\degree)=(15)/(\sin70\degree)=(AB)/(\sin45\degree) \\ \\ \therefore BC=14.5 \\ \therefore AB=11.3 \end{gathered}`