Question

While flying a kite at the beach, you notice that you are 100 yards from the kite’s shadow, which is directly beneath the kite. You also know that you have let out 150 yards of string. How high is the kite?

Answer 1

alright so here you would use the Pythagorean theorem. a^2+b^2=c^2.
You can create a straight line from the kites shadow to where you are standing. Then you can also create a straight line from the string you are holding to where it is attached to the kite.
lastly, you can draw a last line from the kite in the sky to its shadow on the ground.
you have created a triangle.
you know that from the string in your hand to where it is attached to the kite is 150 yards, this is also the hypotenuse.
you also know that you are 100 yards from the kites shadow on the ground.
this is one of the legs.
so your equation would look something like 100^2+b^2=150^2

simplify to 10000+b^2=22500
subtract 10000 from each side
b^2=12500
square root both sides
your answer is approximately 111.8 yards

Answer 2

In this problem, we are given that:

1) The distance from you (the person flying the kite) to the kite's shadow on the ground is 100 yards.

2) You have let out 150 yards of kite string.

Notice that the line drawn from you to the kite's shadow on the ground, the kite string, and an imaginary line from the kite straight down to its shadow form a right triangle. Here, the kite string represents the hypotenuse (the longest side of the right triangle), the line from you to the kite's shadow on the ground is one of the legs, and the height of the kite (the line from the kite straight down to its shadow) is the other leg.

We aim to find the height of the kite, so we will employ the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. So, we can rearrange the formula to find the length of one of the other side (the kite's height in our case) given the length of the hypotenuse and the other side. The formula for this is:

kite's height (c) = \(\sqrt{hypotenuse^{2} - shadow-distance^{2}}\)

Software used for the calculation provided us the values. Plugging these values into this equation:

kite's height (c) = \(\sqrt{150^{2} - 100^{2}}\) = \(\sqrt{22500 - 10000}\) = \(\sqrt{12500}\) = 111.8 yards

So, the height of the kite above ground is approximately 111.8 yards.

Answer: 111.8 yards.