Answer
$5808ft$
Work Step by Step
Step 1. Draw a diagram as shown in the figure (not to scale) where h is the height of the mountain, BC=1000ft
Step 2. As $AD\parallel BE$, we have $ \angle ABE=32^\circ$ and $ \angle ACE=35^\circ$
Step 3. In the right triangle of $\Delta ABE$, we have $tan32^\circ=\frac{h}{BE}$ and $BE=h\cdot cot32^\circ$
Step 4. In the right triangle of $\Delta ACE$, we have $tan35^\circ=\frac{h}{CE}$ and $CE=h\cdot cot35^\circ$
Step 5. As BC=1000ft, we have BE−CE=BC and $h\cdot cot32^\circ-h\cdot cot35^\circ=1000$
Step 6. Solve the above equation as$(cot32^\circ-cot35^\circ)h=1000$ or $(1.60033−1.42815)h=1000$ which gives $h\approx5808ft$
