Question

I need help with these 2 questions.

A) Write and solve a proportion to determine the height of the cell phone tower. Please show your work.

B) What is the height of the tower in meters?

Answer 1

A).
`(1.8)/(6) = (height)/(60)`

B). 18 meters tall

Explanation:

We see TWO right triangles in this problem:

1. the one with the man and the 6m
2. and the one with the phone tower and the 60m

These triangles are proportional so we can make a ratio out of them

the height of the man over the side of the triangle (6m)

and the height of the tower over the length of its triangle (60m)

Set these equal to each other to complete part A

`(1.8)/(6) = (height)/(60)`

And by using cross multiplication (which is what you do for ratios), solve for h!

For a quick example of cross multiplication, I've attached a picture.

Now let's do it!

1.8 × 60 = 6 × h

108 = 6h

108/6 = h

h = 18

The height of the cell phone tower is 18 meters.

Answer 2

Part (A)

Because the right triangles are similar, we can form two ratios P/Q and R/S that are equal to one another.

P/Q = R/S

where,

• P = height of the person
• Q = horizontal distance person is from the left-most corner
• R = height of the tower
• S = horizontal distance the tower is from the left-most corner

In this case,

• P = 1.8 meters
• Q = 6 meters
• R = unknown, we'll use variable h
• S = 60 meters

Therefore, we go from this

P/Q = R/S

to this

(1.8)/6 = h/60

Other equations can be set up. This means there are other possible final answers. The key is to have things be consistent. The equation I've set up has the vertical components as the numerators, while the horizontal components are the denominators.

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Answer: (1.8)/6 = h/60

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Part (B)

Let's cross multiply and solve for h.

(1.8)/6 = h/60

1.8*60 = 6h

108 = 6h

6h = 108

h = 108/6

h = 18

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Answer: 18 meters