a) How far away is the office building from the One World Trade Center? b) How tall is the office building? Round to the nearest foot.

Question

One World Trade Center is to be the centerpiece of the rebuilding of the World Trade Center in New York City. The tower will be 1368 feet tall. The angle of elevation from the base of an office building to the top of the tower is 34 degrees. The angle of elevation from the helipad on the roof of the office building to the top of the tower is 20 degrees.

Answer 1

Construct a trapezium, ABCD for this question;

 

AB is a vertical line representing WTC1 and is 1368 ft high

 

DC is a vertical line representing the office building a perpendicular distance of AD away from the foot of WTC1

 

Connect CB and BD;  ADB = 34 degrees.

 

 Draw a horizontal line from C to intersect AB at E, the angle ECB is 20 degrees

 

a) From your trig. ratios AB/AD = OPP/AD = Tan 34 = 0.675; therefore AD = 1368/0.675 = 2028 ft

 

b)   EB/EC = Tan 20 = 0.364;

 

therefore EB = 2028 * 0.364 = 738 ft; hence AE = DC = height of bldg = AB - EB = 1368 - 738 = 630 ft