Answer
The height of the radio tower is 196.8 ft long
Step-by-step explanation:
Let the height of the radio tower be x
Given that
The base of the radio tower is 8.2ft long
The height of the 4th grader = 36 ft long
The base of the 4th grader = 1.5 ft long
To find the value of x
Since the figures are similar
We will be applying the triangle similarity theorem
Let assume the height of the radio tower is AB
The base of the radio tower is BC
Also, let the height of the 4th grader be XY
Let the base of the 4th grader be YZ
This implies that
AB = x
BC = 8.2
XY = 36
YZ = 1.5
Applying the triangle similarity theorem
We will have
AB / XY = BC / YZ
x / 36 = 8.2 / 1.5
Cross multiply
x * 1.5 = 8.2 * 36
1.5x =295.2
Divide both sides by 1.5
1.5x/1.5 = 295.2/1.5
x = 295.2 / 1.5
x = 196.8 ft long
Hence, the height of the radio tower is 196.8 ft long
