A balloon is at an altitude of 2000ft. The angle of depression from the balloon to a large rock in the center of a pond is 22 degrees, 20minutes. How far horizontally must the balloon move to be directly over the rock?
Can anyone get me to the answer on this please? Thanks!
2006-11-13 11:58:23 · 3 answers · asked by mdetaos 3 in Science & Mathematics ➔ Mathematics
Draw a diagram with an upside down right triangle. Go out from the balloon to a point directly over the pond. Call this distance x. Then go down a distance of 2000 ft. You have an angle of depression of 22° 20' which is the same as 22 1/3°.
So you have the opposite side, and want to compute the adjacent side of the triangle. From the mnemonic SOH-CAH-TOA for a right triangle:
tan(angle) = opposite / adjacent
The opposite side is the 2000 ft. The adjacent side is x ft. The angle is 22 1/3°
So tan(22 1/3°) = 2000 / x ft.
x = 2,000 / tan(22 1/3°)
x = 2,000 / 0.4108
x ≈ 4,868 ft.
2006-11-13 12:08:36 · answer #1 · answered by Puzzling 7 · 0⤊ 0⤋
tan(22 1/3) = 2000/x
x = 2000 / tan(22 1/3)
x = 4,868 ft.
2006-11-13 20:04:54 · answer #2 · answered by Anonymous · 0⤊ 0⤋
first you need to find the cotangent (1/tangent) of 22degrees 20 min
it is:2.434
then multiply by the 2000 ft
2.434x2000=
4868ft
2006-11-13 20:08:50 · answer #3 · answered by William S 2 · 0⤊ 0⤋