Can you tell me how to do this exactly?

Question

Amy is standing next to a 24–foot billboard. She starts walking away at a rate of 2 feet per second. After

6 seconds, she stops because she notices that the end of her shadow meets the end of the billboard’s

shadow. If Amy is 5 feet tall, how long is the billboard’s shadow?

Round to the nearest tenth of a foot if necessary.

Answer 1

This problem could be solved using similar right triangles.

1st right triangle is the billboard height-shadow-light

2nd right triangle is Amy height-shadow-light

Two similar right triangles:

hypotenuses are the light from the tops of billboard and Amy.

opposite sides are the height of both of them.

adjacent sides are the shadows of both of them.

Both shadows meet at the apex of the given angle.

Now let x be length the billboard's shadow and y be the length of Amy's shadow.

Then we have:

x/y = 24ft/5ft ratio of sides eq. 1

also x-y = 2 ft/s x 6s = 12 ft two shadows overlapping eq. 2

Solve the equations:

x = (24/5)y eq. 3

substituting eq. 3 into eq. 2

(24/5)y - y = 12 ft

4.8 y - y = 12 ft

3.8 y = 12 ft

y = 3.2 ft

put value of y into eq. 3

x = 24/5 • 3.2 ft

= 15.36 ft

= 15 ft// answer

It will be very helpful to draw out the diagram of these two similar triangles.

Answer 2

Hi Deinoncychus,

Basically, we are going to have two similar triangles. Draw one line and label it 24 ft. then for the distance walked to the end of the shadow. Distance= rate * time. . You have the rate and you have the time. substitute and solve.

Your second triangle has a height of 5 ft. You can set up the proportions to solve for the length of the shadow.

I got you started. Draw it out now. I am here if you have further question.

Mona