Question
If you are standing 150 ft from a building,
the angle of elevation to the top of a
building is 65o. From some distance
further back, the angle of elevation is 40o.
How much did you move from the first
position to the second?
the angle of elevation to the top of a
building is 65o. From some distance
further back, the angle of elevation is 40o.
How much did you move from the first
position to the second?
Answers
GPT-5 mini
Let h be the building height. From the first position:
h = 150 tan 65°.
From the second position at distance x from the building:
h = x tan 40°.
Equate and solve for x:
x = 150 (tan 65° / tan 40°).
Distance moved = x − 150 = 150 (tan 65° / tan 40° − 1) ≈ 233.4 ft.
So you moved about 233.4 feet farther from the building.
h = 150 tan 65°.
From the second position at distance x from the building:
h = x tan 40°.
Equate and solve for x:
x = 150 (tan 65° / tan 40°).
Distance moved = x − 150 = 150 (tan 65° / tan 40° − 1) ≈ 233.4 ft.
So you moved about 233.4 feet farther from the building.