Question

A 1010​-ft vertical post casts a 2020​-in. Shadow at the same time a nearby cell phone tower casts a 115115​-ft shadow. What is the first step to find the height of the cell phone​ tower? How tall is the cell phone​ tower? The cell phone​ tower's height is

Answer 1

Answer:

690862 ft

Step-by-step explanation:

Consider Figure 1.1 in the attachment, first all dimensions must be in the same unit.

12 inches = 1 feet

2020 inch = 168.33 feet

Next, using trigonometric ratio,

$tan \theta = opposite/adjacent = 1010/168.33$

Therefore:  $\theta = arctan(1010/168.33)=80.54$

Now at a particular point in time, the angle of elevation of the sun is the same on all objects, therefore the angle of elevation of the mast is the same as that of the vertical post.

Therefore $\theta = 80.54$  in figure 1.2

$tan 80.54 = opposite/adjacent = x/115115$

x= 115115 X tan80.54 =690862ft.

Therefore the height of the phone tower is 690862ft