Observers in two towns A and B on either side of an h = 19,000 -ft mountain meas

Question

Observers in two towns A and B on either side of an h = 19,000-ft mountain measure the angles of elevation between the ground and the top of the mountain. See the figure below. Assuming that the towns and the mountaintop lie in the same vertical plane, find the horizontal distance between them where = 25° and = 44°. (Round your answer to two decimal places.)

Observers in two towns A and B on either side of an h = 19,000-ft mountain measure the angles of elevation between the ground and the top of the mountain. See the figure below. Assuming that the towns and the mountaintop lie in the same vertical plane, find the horizontal distance between them where

Explanation / Answer

Let S be the bottom of the hill.

tan(a) = h / AS

AS = h / tan(a)

tan(b) = h / SB

SB = h / tan(b)

AS + SB = AB = h/tan(a) + h/tan(b)

AB = h*(1/tan(a) + 1/tan(b) )

= 19000*( 1/tan(25) + 1/tan(44) )

= 60420.71 ft

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