Question

Two buildings on level ground are 200 feet apart. From the top edge of the shorter building, the angle of elevation to the top of the taller building is 24 degrees, and the angle of depression to the bottom of the taller building is 35 degrees. How tall is each building?

a. 100 ft, 200 ft

b. 140 ft, 229 ft

c. 150 ft, 215 ft

d. 125 ft, 225 ft

Answer 1

Let S be the point on the shorter building be the point from which measurements are taken.

Let T be the point on the top of the taller building and B the point at the bottom.

This gives us a triangle STB where TB is the height of the taller building. The horizontal line from S to TB is a perpendicular SM, where SMB is a right angle. Let the height of the shorter building be SP where SPB is a right triangle (SPB is the right angle). SPB, SMB and STM are all right triangles, where the angle measures are TŜM=24°, SB̂P=MŜB=35°. SM=PB=200 feet. PŜB=SB̂M=90-35=55°.

SP/PB=tanSB̂P,

shorter height MB=SP=PBtanSB̂P=200tan35=140ft approx.

TM/SM=tanTŜM,

difference in height of the buildings TM=SMtanTŜM=200tan24=89ft approx. Height of taller building=TM+MB=TM+SP=89+140=229ft.

Answer b.