SOLUTION: From a stationary hot-air balloon 500ft above the ground, two sightings of a lake are made. One at the farthest end of the lake at an angle of depression of 25 degress and another

Question 114160: From a stationary hot-air balloon 500ft above the ground, two sightings of a lake are made. One at the farthest end of the lake at an angle of depression of 25 degress and another at the nearest end of the lake at an angle of depression of 65 degress. How long is the lake?
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
From a stationary hot-air balloon 500ft above the ground, two sightings of a lake are made. One at the farthest end of the lake at an angle of depression of 25 degress and another at the nearest end of the lake at an angle of depression of 65 degress. How long is the lake?
----------------
Draw the picture.
You have two right triangles; let the base of the triangle with
the 65 degree angle be x; let the base of the triangle with the
25 degree angle be y.
-----------------------------
x + y is the length of the lake.
--------------------------
x = 500/tan(65)
y = 500/tan(25)
-------------------
x+y = 233.15+ 1072.25 ft
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Length of lake = 1305.41 ft.
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Cheers,
Stan H.
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