The following picture represents an explanation to the given question:
CD represents the beacon
We need to find the distance AB
The measure of the angle C = 90
At the triangle BCD,
The measure of the angle CDB = 90 - 21 = 69
Using the sine law, we will find the length of BD
So,
[tex]\begin{gathered} \frac{BD}{\sin90}=\frac{CD}{\sin 21} \\ BD=CD\cdot\frac{\sin90}{\sin21}=\frac{CD}{\sin 21} \end{gathered}[/tex]At the triangle ABC
The measure of the angle CDA = 90 - 10 = 80
So, the measure of the angle ADB = angle CDA - angle CDB = 80 - 69 = 11
At the triangle ADB, using sin law:
[tex]\begin{gathered} \frac{AB}{\sin D}=\frac{BD}{\sin A} \\ \\ AB=BD\cdot\frac{\sin D}{\sin A}=BD\cdot\frac{\sin 11}{\sin 10} \end{gathered}[/tex]substitute with the value of BD and CD s
So,
[tex]AB=\frac{CD}{\sin21}\cdot\frac{\sin11}{\sin10}=\frac{113\cdot\sin 11}{\sin 21\cdot\sin 10}=346.4798[/tex]Rounding the answer to the nearest foot
So, the answer will be AB = 346 ft
