Question

A= 9 b= 7 and c= 12 Find A , B and C .solve the triangle. Round to the nearest tenth if necessary..

Answer 1

First notice that angle C is a right angle, then:

`\measuredangle C=90`

Now, since this is a right triangle, we can find the measure of angle A using the trigonometric function sine:

`\sin \theta=\frac{\text{opposite side}}{hypotenuse}`

In this case, we have the following:

`\begin{gathered} a=9 \\ c=12 \\ \sin A=(a)/(c)=(9)/(12)=(3)/(4) \\ \Rightarrow A=\sin ^(-1)((3)/(4))=48.6 \\ \measuredangle A=48.6\degree \end{gathered}`

Since the sum of the interior angles of a triangle equals 180, we can find the measure of angle B by solving the following equation:

`\begin{gathered} \measuredangle A+\measuredangle B+\measuredangle C=180 \\ \measuredangle A=48.6 \\ \measuredangle C=90 \\ \Rightarrow48.6+\measuredangle B+90=180 \\ \Rightarrow138.6+\measuredangle B=180 \\ \Rightarrow\measuredangle B=180-138.6=41.4 \\ \measuredangle B=41.4\degree \end{gathered}`

therefore, angle A measures 48.6 degrees and angle B measures 41.4 degrees