Question

To measure a stone face carved on the side of a​ mountain, two sightings 600 feet from the base of the mountain are taken. If the angle of elevation to the bottom of the face is 42degrees and the angle of elevation to the top is 45degrees​, what is the height of the stone​ face?

Answer 1

• 41.2 ft

Step-by-step explanation:

horizontal distance of sighting from the base of the mountain (A) = 600 ft

angle of elevation to the bottom of the face = 42 degrees

angle of elevation to the top of the face = 45 degrees

find the height of the face

• from the diagram attached we can see that the point of sightings, the base of the mountain and the bottom of the face form a right angle triangle (triangle ABC)

• we can also see that the point of sightings, the base of the mountain and the top of the face form another right angle triangle (triangle ABD)
• therefore we first need to find the sides BC and BD and then subtract BC from BD to get the height of the face.

• for triangle ABC

cos θ = AB / BC

cos 42 = 600 / BC

BC = 600 / cos 42

BC = 807.4 ft

• for triangle ABD

cos θ = AB / BD

cos 45 = 600 / BD

BD = 600 / cos 45

BD = 848.5 ft

• height of the face = BD - BC = 848.5 - 807.4 = 41.2 ft