Step-by-step explanation:
The attached figure shows the whole scenerio.
BC = 5280 feet
We need to find height of the mountain. i.e. AB and the hiking distance i.e. AC.
Using trigonometry as follows :
[tex]\tan\theta=\dfrac{AB}{BC}\\\\AB=\tan(25.27)\times 5280\\\\AB=2492.46\ \text{feet}[/tex]
The height of the mountain is 2492.46 feet
Also,
[tex]\sin\theta=\dfrac{AB}{AC}\\\\AC=\dfrac{AB}{\sin\theta}\\\\AC=\dfrac{2492.46}{\sin(25.27)}\\\\AC=5838.72\ \text{feet}[/tex]
Hence, Height of the mountain = 2492.46 feet
hiking distance= 5838.72 feet.
