AbdulrehmanN554943 AbdulrehmanN554943
  • 03-11-2022
  • Mathematics
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What is the distance from A to B given

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AdyleeT203307 AdyleeT203307
  • 03-11-2022

Using the triangle sum theorem, we can conclude:

[tex]\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}[/tex]

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

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

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