Aradio tower casts a shadow 8 feet long at the same time that a vertical yardstick casts a shadow half an inch long. how tall is the radio tower?

The height of radio tower is 576 feet approximately

Solution:

Given that, radio tower casts a shadow 8 feet long

At the same time that a vertical yardstick casts a shadow half an inch long

To find: height of radio tower

Let "x" be the height of radio tower

length of shadow of tower = 8 feet

Length of shadow of stick =

Convert inch to feet

Thus,

Length of shadow of stick = 0.0416 feet

Length of vertical yard stick = 3 feet (since 1 yard = 3 feet )

Therefore, by proportion we get,

Substituting the values we get,

Thus height of radio tower is 576 feet approximately

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2