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 th
e 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?
1 answer:
Answer:
- 41.2 ft
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
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