how do you find the shadow of a 5 ft tall person if he or she is 30 ft away from a 20 foot tall street light?

Question

the street light and groung make a 90 degree angle and the light from the street lamp and the persons shadow makes a right triangle

Answer 1

This is a basic geometry question which uses the axiom that the ratio of similar triangles are equal. This means that the ratio of the triangle created by the person's shadow and the triangle created by the light with respect to the person should be equal.

|
|
|
20_________________ |
|___________________5
|________30_________|_____X_______

If the length of the shadow created by the person is equal to

X

then the total distance to the head of the shadow from the light pole will equal

30 + x

Since the ratio of the triangles should be equal we get this equation.

20/(30 + x) = 5/x

Doing the math, you get

20x = 150 + 5x

which simplifies to

15x = 150

which means

x = 10

Therefore, the length of the shadow is 10 feet long.

p.s. People, these ARE NOT congruent triangles. Congruent triangles have three sides that are congruent, meaning equal, and three angles that are congruent. This problem demonstrates the properties of SIMILAR triangles.

Answer 2

Look behind them?
Just kidding. Draw a nice, long horizontal line for the ground. Then draw a vertical line up from the ground at one end. At the top, make a circle. This is the light. Then somewhere in the middle of the ground, draw a shorter line with a circle. This is your person (and their head).
Draw a line connecting the center of the light to the person's head, then continue to the ground. You now have two triangles that are congruent: they have the same 3 angles. You also have a quadrilateral with two right angles. Hmm... not quite enough to solve this problem. What next?
Draw a line parallel to the ground from the person's head to the light post and you have a 3rd congruent triangle sitting atop a 5x30 rectangle. I say congruent, because in all of the triangles, all 3 angles are the same. You don't actually need to know the other 2 angles to solve the problem. It's not geometry at this point, just simple algebra.

This ought to be enough for you to solve the rest of the problem. You didn't ask for an answer, right, just the method to solve the problem.

Answer 3

The person forms a right triangle with her shadow.
You don't know the length of the shadow, so call it "s"

The ratio of her height to the shadow length = 5/s

The person and her shadow form a right triangle with the street light.

The ratio here = 20/(30 + s)

Since these are both similar right triangles, equate the two ratios:

20/(30 + s) = 5/s

20s = 150 + 5s
15s = 150
s = 10 feet, the length of the shadow

Answer 4

First you visualize the problem-it helps to draw it out. If you do this you can calculate the slope of the line from the top of the light pole to the person-ie, (20-5)/30=0.5 = slope = rise over run. Then you make a new equation for the light ray from the top of the person to the ground, using the same slope. So rise over run=slope = 0.5 = 5/x Solving this you get x=10 so the shadow would be 10 feet long.

Answer 5

the shadow is ten feet long

15 rise,30 run for the street lamp to the top of the body, because the shadow starts at the head, not the feet.

transfer to 5 rise 10 run on the shadow

Answer 6

Hypotenuse theorum.

A squared + B squared = C squared.

You take the two distances you know, add them. Then you square your answer and that's the answer.

The hypotenuse of any right triangle is equal to the square root of the sum of the remaining sides.

Answer 7

look around their feet. The shadow always starts at the feet. Are you sure you asked the question right?

Answer 8

hmmm... if theyre both congruent triangles, you should be able to compare them, right? so i would say 20 is to 30 as 5 is to x.
which comes out to 7.5.
did i do something wrong? what am i missing?

Answer 9

there wouldnt be a shadow, the person would be outside the cone of light, surely ????

or if there were a shadow, it would be a very small shadow

Answer 10

(20/30) = (5/x)
(2/3) = (5/x)
2x = 15
x = 7.5ft