According to the architect's design, the angle of elvation from a point on the ground to the top of the 40-foot tower is 56º. The angle of elvation from the groud point to the top of the building is 42º. The maxium allowed height of any structure is 100 feet. Will the city allow the building of this tower? Explain.
Nope....building + tower will be 101.86 ft tall ....assuming tower is on top of the building.
Tan 56 = (h+40)/d h = height of building d = distance from point to base of building
Tan 42 = h/d
d = h/tan42 = 1.1106 h substitute this into the first equation
Tan 56 = 1.4826 SUbstitute this into the first equation too:
1.4826 = (h+40)/1.1106h
1.6465 h = h+40
,6465h = 40
h = height of building = 61.868 ft add to this the tower height of 40 ft results in 101.86 ft tall ....too tall.