You are traveling toward a mountain at 75 km/hr. You stop and look up to the top of a mountain. The angle of elevation from the ground to the top of the mountain is 0.026 radians. Twenty minutes later, the angle of elevation is 0.031 radians. About how tall is the mountain? Show all work! A picture may help.
2007-02-18 15:35:49 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Physics
I assume you are travelling on level ground. In 20 minutes you can travel 75/3 = 25km
Let
h = height mountain
25 + x = horizontal distance to mountain peak at time = 0
x = horizontal distance to mountain peak at time = 20 minutes
We have
tan(0.026) = h/(25 + x)
tan(0.031) = h/x
Solving for x.
tan(0.026) = h/(25 + x)
(25 + x)tan(0.026) = h
25tan(0.026) + xtan(0.026) = h
x = h/tan(0.026) - 25
tan(0.031) = h/x
x = h/tan(0.031)
Set the two equations for x equal and solve for h.
x = h/tan(0.026) - 20 = h/tan(0.31)
h{1/tan(0.026) - 1/tan(0.031)} = 25
h = 25 / {1/tan(0.026) - 1/tan(0.031)}
h = 25 / {cot(0.026) - cot(0.031)}
h = 4.0289174 km = 4028.9174 meters
The mountain is 4028.9174 meters high.
2007-02-18 17:05:36 · answer #1 · answered by Northstar 7 · 0⤊ 0⤋
2 as in 2 points
2007-02-18 23:51:47 · answer #2 · answered by Fire Lt. 4 · 0⤊ 1⤋
the mountain is 43,601.60 meters tall. Got it done using sine law first then the trigonometric function of sine.
(how can paste a figure here?)
2007-02-18 23:58:55 · answer #3 · answered by Puzzledmind 3 · 0⤊ 0⤋
75/26= 2.88
75/31=2.42
find the difference of them both
2.88-2.42= .46
.46*75km
is your answer
2007-02-18 23:39:52 · answer #4 · answered by Anonymous · 0⤊ 1⤋
ya im not answering this but are you still moving during those twenty minutes?
2007-02-18 23:39:08 · answer #5 · answered by A 3 · 0⤊ 1⤋
sorry buddy im only in algebra
2007-02-18 23:38:24 · answer #6 · answered by Not Just Another Person 2 · 0⤊ 1⤋