From the top of the Metro Building, the angle of elevation of the top of the Gammapro Building is 24° and the angle of depression to the foot of the Gammapro Building is 56°. If the buildings are 45 m apart, determine the height of each building to the nearest meter.

Answer 1

Diagram:
Draw a rectangle with the vert. sides representing the ht. of the Metro Bldg.(h1).and hor. sides are the distance between bldgs.(45m). Draw a diagonal from lower left to upper right and notice that the alternate interior angles are equal(56o).Extend the vert. side on the left and label it h2.

Draw the line of sight from the top of h2 to the top of Metro Bldg. The angle it makes with the hor. is 24o.

Tan56 = h1/45.
h1 = 45*Tan56 = 67 m. = Ht. of Metro bldg.

Tan24 = h2/45.
h2 = 45*Tan24 = 20.0 m.

h1 + h2 = 67 + 20 = 87 m. = Ht. of Gammapro Bldg.