SOLUTION
Let the height of the mountain be z
Hence the height of the mountain is:
[tex]\begin{gathered} \sin37^{\circ}=\frac{h}{1450} \\ h=872.6 \end{gathered}[/tex]
From the figure it follows:
[tex]\begin{gathered} \cos37^{\circ}=\frac{DA}{1450} \\ DA=1158.0 \end{gathered}[/tex]
Also from the figure it follows:
[tex]\tan22^{\circ}=\frac{h}{DB}[/tex]
Reall h=872.6.
Substitute h=872.6 into the equation:
[tex]\begin{gathered} \tan22^{\circ}=\frac{872.6}{DB} \\ DB=\frac{872.6}{\tan22^{\circ}} \\ DB=2159.8 \end{gathered}[/tex]
Using segment addition it follows:
[tex]DB=DA+AB[/tex]
Substitute DA=1158.0 and DB=2159.8 into the equation:
[tex]2159.8=1158+AB[/tex]
Solve for AB:
[tex]\begin{gathered} AB=2159.8-1158 \\ AB=1001.8 \end{gathered}[/tex]
Therefore the distance from A to be is 1001.8 feet.
