Question

A cell phone tower in a field casts a shadow of 100 ft. At the same time, a 4 ft 6 in post near the tower casts a shadow of 3 ft 4 in. Find the height of the tower in feet. (Hint: make a drawing) a. 145 ft c. 100 ft b. 76 ft d. 135 ft Please select the best answer from the choices provided

Answer 1

135 feet

Explanation:

We have 2 similar triangles here, so

3 1/3 / 100 = 4.5 / h

= 100 * 4.5 / (10/3) = 100*4.5 * 3 / 10

h = 135 feet

Answer 2

Answer: d. 135 ft

Explanation:

Given: A cell phone tower and post are standing vertical at the same time.

Then they are forming two similar triangles.

We know that the corresponding sides of similar triangles are proportional.

We know that 1 foot = 12 inches.

Then, Height of post =4 ft. 6 in =
`4*12+6=54\ \text {inches}`

Post's shadow = 3 ft 4 in. =
`3*12+4=40\text{ inches}.`

According to the given question, we have :-

`\frac{\text{Height of tower}}{\text{Tower's shadow}}=\frac{\text{Height of post}}{\text{Post's shadow}}\\\\\Rightarrow\ \frac{\text{Height of tower}}{100}=(54)/(40)\\\\\Rightarrow\ \text{Height of tower}=(54*100)/(40)=135\text{ ft.}`

Hence, the height of tower = 135 ft.