SOLUTION: An airplane is flying at an elevation of 12,000 feet before diving at an angle of depression of 45 degrees for 25 seconds. The plane is traveling at an average rate of 260 miles pe

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Question 549011: An airplane is flying at an elevation of 12,000 feet before diving at an angle of depression of 45 degrees for 25 seconds. The plane is traveling at an average rate of 260 miles per hour during the dive. At what elevation does the plane end the dive?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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An airplane is flying at an elevation of 12,000 feet before diving at an angle of depression of 45 degrees for 25 seconds. The plane is traveling at an average rate of 260 miles per hour during the dive. At what elevation does the plane end the dive?
:
This can be solved as a right triangle using the sine of 45 degrees, where:
the change altitude (a) is the side opposite and
the distance traveled in the dive is the hypotenuse (h)
:
We want the elevation change in feet.
Change distance of the dive to feet traveled in 25 seconds: (3600 sec in 1 hr)
h = %28%28260%2A5280%29%29%2F3600 * 25 = 9533.33 ft
:
sin(45) = a%2F9533.33
a = sin(45)*9533.33
a = 6741.1 ft change in elevation
therefore
12000 - 6741.1 = 5,258.9 ft altitude at the end of the dive