Question

A person 6 ft. tall is standing near a street light so that the ratio of his height to the pole is 3/5. (a) Find the length of the pole. (b) if the person's head is exactly 5 ft from the light bulb, how far is the person from the pole? (5) how long is the shadow?.. I just the the concept of how to solve the problem.

Answer 1

the pole, the person and the shadow form two similar triangles one 'inside' the other.
you can use the property of similar triangles to solve this problem ie corresponding sides are in the same ratio. In this case the ratio is 3:5.

Answer 2

Could you show me the formula in solving this problem. just the formula no need for the answer because I am the one who do about it.

Answer 3

I have to say, I don't like how this question is worded. I assume the first statement should read the ratio of the person's height to the pole's height is 3/5. (I don't like "so that" - where he stands won't affect the ratio.
So part (a) is a ratio question
\[\frac{personht}{pole ht}=\frac{3}{5}\]
solve for pole ht.

Answer 4

so the height of the pole is = to 10

Answer 5

Yes. Now part (b). I drew a picture
pole 10 ft high and a 6 ft person near the pole. I interpreted the statement
"the person's head is 5 ft from the light" as the diagonal distance between the top of the pole and the top of the person.

Answer 6

what should I do next?

Answer 7

Figure out how far the person is from the pole. I assume they are asking for the horizontal distance. Hint, draw a line horizontally from the head to the pole, to make a right triangle.

Answer 8

the it will form a triangle that has a height = 4 and hypotenuse = 5?

Answer 9

do know what is the Pythagorean formula for this?

Answer 10

Definitely on the right track. The Pythagorean formula is so important you should really really know it! For a right triangle with 2 sides a,b and hypotenuse c
\[a ^{2}+b ^{2}=c ^{2}\]

Another thing to know (because people always use it in these questions) is that
3,4, 5 form a right triangle. It saves time if you know this.

Answer 11

As for part (c), extend the line from the light to head to ground. form a 2nd triangle by drawing a horizontal line from the person's feet to the tip of the shadow. Now it is another ratio problem. The 3,4,5 triangle is similar to the 2nd triangle.

Answer 12

Am i right that the eqution for ci is 4/10=5/x?

Answer 13

To find the answer to part (b), how far is the person from the pole (horizontal distance) we use Pythagoras. Label one side a, the other side b, the hypotenuse c.
Let's call the vertical side a, which we know is 4 (height of pole minus ht of man)
c=5 (they told us this)
so solve
\[4^{2}+b ^{2}=5^{2}\]
b is the horizontal distance between the pole and the man

Answer 14

b=3

Answer 15

Now on to part (c). Take a shot at it...

Answer 16

on the third problem what is the equation?

Answer 17

Did you draw the picture, with two triangles (the 3,4,5 one) and a 2nd one formed by the person and the shadow?

Answer 18

yup i did!

Answer 19

Do you know about similar triangles ? They are triangles with different sized legs but their corresponding angles are equal. Exact same shape but different sizes.
If you know geometry you can prove we have two similar triangles, so their corresponding sides form ratios.

Answer 20

so the ratio must be 3/5 also?

Answer 21

If you are referring to the height of the person to that of the pole (= 3/5), no. at least I don't see an easy way to use it.

What you do is look at the two triangles. One you know completely (I mean you know the length of each side). Look at the other triangle. One side you know. Another side you want to know.

You also know that (side a of triangle1)/(side a of triangle 2) = (side b of triangle 1)/(side b of triangle 2)

Answer 22

x=4.5? the side b of triangle 2= 7.5?

Answer 23

then the hypotenuse of the 2nd triangle is 12.5?

Answer 24

What is x? I mean, it's the distance from where to where?

Answer 25

thank you so much for your help. but actually the problem that we solved were just 5% of all the items that I must answer.

Answer 26

3+x the distance of the side b of triangle 2

Answer 27

Here's a picture. The legs of the same color correspond to one another. So you can form ratios.
The length of the shadow (of the man, not the pole) is the distance x in the picture.

Answer 28

So it looks like this is a dumb question, because they don't say what shadow they want!!
But if you see a million questions like this, it's typically the person's shadow they want to know.

Answer 29

OK. You did get the right answer. Hopefully the rest of the questions are similar to this one.

Answer 30

actually there are only two similar problems in my assignments. including this one. others were another concept of analytic geometry.