Question

Please Help!!!
Kyle is 52 inches tall. The distance from the top of his head to the tip of his shadow is 60 inches. Approximately how long is Kyle's shadow?


A.
30 inches







B.
40 inches







C.
79 inches







D.
102 inches

Answer 1

Have you heard of the pythagorean theorem?

Answer 2

Yes

Answer 3

Well not really I mean I kind of know but I never really understood it.

Answer 4

c^2 = a^2 + b^2

c is the hypotenuse, 60in, and a is Kyle's height of 52in. You are looking for side b, which is the length of his shadow:

(60)^2 = (52)^2 + x^2

solve for x

Answer 5

Ahh, ok, then I'll teach you about probably one of the most important things in math!



So if you have a right triangle (a triangle where one angle is 90 degrees) then you can use the pythagorean theorem.

What it says is that if you take the two sides that are connected by the right angle, they are called the legs, which I've labeled with lengths "a" and "b". If you take them and square the numbers then add them together it equals the square of the hypotenuse which is the other side not touching the right angle

\[a^2+b^2=c^2 \]

Answer 6

Please explain how that has anything to do with this problem.

Answer 7

@Kainui

Answer 8

Look at the picture and what larry wrote. The shadow and the person standing forms a right triangle. Since you know 2 of the distances you can plug them in to the pythagorean theorem to solve for the other side you don't have.

Answer 9

As you can see that his figure within the visual is showing a right triangle. And on one leg we don't know how much is the measurement. That's when the Pythagorean Theorem comes handy. We use: a^2+b^2= c^2 ( where is the hypotenuse, or the largest side length of the triangle).

Answer 10

Are you with me so far?

Answer 11

Yeah

Answer 12

a and b can be any of the legs. However you must maintain the fact that c is always the hypotenuse, so you cannot give any number for that. We know the hypotenuse (which is 60 inches) and one of the legs (which is 52 inches). We can set the equation up as 52^2+b^2 (which is the unknown measurement of the leg) = 60^2. Solve for b^2.

Answer 13

Ok so it is 79 inches? @calculusxy

Answer 14

How did you get that? Explain your way please.

Answer 15

I put it in into the calculator and it gave me 8sqrt(14) for b than I put 8sqrt(14) into the calculator and got 29. Than I added 29 and 52.

Answer 16

@calculusxy