Question

What is the distance from A to B given

Answer 1

Using the triangle sum theorem, we can conclude:

`\begin{gathered} m\angle A+m\angle B+m\angle C=180 \\ 40+m\angle B+50=180 \\ so\colon \\ m\angle B=180-50-40 \\ m\angle B=180-90 \\ m\angle B=90 \end{gathered}`

Now, we can use the law of sines in order to find AB:

`\begin{gathered} (AB)/(\sin(C))=(AC)/(\sin (B)) \\ solve_{\text{ }}for_{\text{ }}AB\colon_{} \\ AB=(\sin (C)\cdot AC)/(\sin (B)) \\ AB=(\sin (50)\cdot100)/(\sin (90)) \\ AB=76.60444431ft \end{gathered}`