Problema Solution
Bob is driving along a straight and level road towards a straight mountain.At some point on his trip he measures the angle of elevation to the top of the mountain and finds it to be 23degrees27'. He then drives 1mile(1mile= 5280 ft) more and measures the angle of elevation to be 34degrees52'. Find the height of the mountain to the nearest foot
Answer provided by our tutors
let 'x' be the distance in feet from Bob's final measurement to a point directly under the mountain peak, then 'x+5280' is the distance in feet from the first measurement
tangent of an angle = 'side opposite' / 'side adjacent'
tangent(23 degrees 27 minutes) = 0.4337
tangent(34 degrees 52 minutes) = 0.6967
let 'h' be the height of the peak in feet:
0.4337 = h/(x+5280)
0.6967 = h/x
solving these equations for 'h':
h = 0.4337(x+5280)
h = 0.6967x
setting the right-sides equal to each other and solving for 'x':
0.4337(x+5280) = 0.6967x
x = 8706.98
the height of the peak is then:
h = 0.6967(8706.98) = 6066
the height of the mountain is approximately 6,066 feet