Question

5. A 64-foot tall monument casts a shadow 16 feet long. If Kyle is standing nearby and is 6'3" tall, find the length of his shadow.​

Answer 1

Using a proportion based on similar triangles, we find that the length of Kyle's shadow is approximately 1.56 feet.

Step-by-step explanation:

The question asks about determining the length of a shadow cast by a person, given the shadow length and height of another object. To solve this, we set up a proportion based on similar triangles. The monument and the person stand up straight, similar to the perpendicular sides of right triangles, with their shadows being the bases.

First, we'll set up the proportion by using the height and shadow length of the monument:

• Height of monument / Length of monument's shadow = Height of Kyle / Length of Kyle's shadow

Substituting the known values, we get:

• 64 feet / 16 feet = 6.25 feet / Length of Kyle's shadow

Now we solve for the length of Kyle's shadow by cross-multiplying:

• 64 feet x Length of Kyle's shadow = 6.25 feet x 16 feet

Dividing both sides by 64 gives us:

• Length of Kyle's shadow = (6.25 feet x 16 feet) / 64 feet = 1.5625 feet

Therefore, the length of Kyle's shadow is 1.5625 feet or about 1.56 feet when rounded to two decimal places.