Apartment complex

Question

An apartment complex is located 55 metres down the street from an office tower. The angle of elevation to the top of the tower, as measured from the roof of the apartment complex, is 58 degrees. From the same spot, the angle of depression to the base of the tower is 36 degrees. Calculate the height of the office tower. Answer to the nearest metre. Use the oblique triangle.

Answer 1

from the roof of the complex draw a horizontal line to the tower

the distance above the horizontal line plus the distance below the horizontal line is the height of the office tower

the 58º angle forms a right triangle and the 36º angle forms another right triangle and they have the horizontal side in common, which is 55 meters in length because it's parallel to the ground distance of 55 meters

use the tangent function

tan58º=x/55 where x is the distance above the horizontal line

tan36º=y/55 where y is the distance below the horizontal line

these distances added together gives the height of the tower

tan58º=x/55

1.6=x/55

x=1.6*55

x=88 m

tan36º=y/55

0.7265=y/55

y=0.7265*55

y=39.957 m

88+39.957=127.957 m is the height of the tower