Question

A lookout tower has been erected on top of a mountain. At a distance of 5.8 km, the angle of elevation from the ground to the base of the tower is 15.7°, and the angle of elevation to the observation deck (on the top of the tower) is 15.9°. How high, to the nearest metre, is the observation deck above the top of the mountain?

Answer 1

The length of the deck above the top of the mountain will be found as follows:
sin θ=opposite/ adjacent

The height of the mountain will be given by:
sin15.7=m/5.8
m=5.8sin15.7
m=1.57 km

The distance from the ground to the top of the deck will be:
sin 15.9=h/5.8
h=5.8sin15.9
h=1.588
The height of the deck will be:
h-m
=1.588-1.57
=0.0018
=18 meters