Question

1. From a window 40 feet above the ground in a certain building, the angle of elevation to a window in a second building is 43°. If the distance between the buildings is 110 feet, about how far above ground level is the second window?
a. 160 feet b. 120 feet c. 140 feet d. 200 feet

Answer 1

Taking the observation point as a vertex. The line to the observed window is the hypotenuse of a right triangle formed with the horizontal distance between the two buildings and the opposite leg to the angle of elevation.

The tangent of this angle is the ratio between the opposite leg and the adjacent leg. And the opposite leg is also the height from the height of the observation window to the observed window.

If h is the height from ground level to the second window, we will call h - 40 to the opposite leg and d to the adjacent leg that is also the horizontal distance between the buildings.

tangent(43º) = 0,93251509 = (h - 40)/d

h = tangent(43º)*d + 40 feet = 0,93251509*110 feet + 40 feet = 142.58 feet

Answer = C.) = 140 feet above the ground level is the second window.

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