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?

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