The given information is:
- Dalvin is watching from a vertical distance of 138 ft above the water.
- He measures an angle of depression to the boat at point A to be 13°.
- At some later time, he takes another measurement and finds an angle of depression of 45° at point B.
We need to find the distance from point A to point B.
A diagram of the problem is:
We can observe two right triangles. We can apply the trigonometric functions to find the adjacent sides of both triangles:
[tex]\begin{gathered} \tan13=\frac{138}{A} \\ A=\frac{138}{\tan13} \\ A=597.7ft \\ \tan45=\frac{138}{B} \\ B=\frac{138}{\tan45} \\ B=138ft \end{gathered}[/tex]
Now we can find the distance from A to B, by subtracting B from A:
[tex]Distance=A-B=597.7-138=459.7ft[/tex]
The answer is 459.7 ft.
