Question

The tower is 1670 feet tall. The angle of elevation from the base of an office building to the top of the tower is 34degrees. The angle of elevation from the roof of the office building to the top of the tower is 23degrees.​
a. How far away is the office building from the​ tower? Assume the side of the tower is vertical.​
b. How tall is the office​ building?

Answer 1

Answer:

A)distance of office building from the​ tower = 2475.9 ft

B)Height of building: 768.77 ft

Step-by-step explanation:

Suppose, we construct a trapezium, ABCD for this question.

Where;

AB is a vertical line representing T1 and is 1670 ft high

DC is a vertical line representing the office building a perpendicular distance of AD away from the foot of T1

Now, we are told that the angle of elevation from the base of an office building to the top of the tower is 34°. Thus connecting CB and BD, we have angle ADB = 34°

Now, if we draw a horizontal line from C to intersect AB at E, the angle ECB is 23°

a) from the attached image, using trigonometric ratios, we have; AB/AD = tan 34°

Thus; 1670/AD = 0.6745

AD = 1670/0.6745

AD = 2475.9 ft

b) Also, from the diagram

EB/EC = Tan 23° = 0.4245

therefore; EB = 2475.9 x 0.364

EB = 901.23 ft

Now, AE = DC = height of bldg = AB - EB = 1670 - 901.23 = 768.77 ft