Question

A object 6.3 feet tall casts a shadow of 18.9 feet long, so a oject that is 13.8 feet tall casts a shadow of?

Answer 1

I'm assuming the angle of the sunlight remains constant.

you can visualize these shadows as similar right triangles, where the short vertical legs are the objects, and the longer horizontal legs are the shadows themselves. because they are similar triangles, the corresponding sides are proportional to one another. that means:

object 1 / shadow 1 = object 2 / shadow 2
6.3 / 18.9 = 13.8 / x
x is the shadow of the second object, the one whose shadow we don't know yet.
solve the proportion by cross-multiplication:
6.3x = 18.9*13.8
6.3x = 260.82
x = 41.4

Answer 2

Use similar triangles (see the picture I drew at the bottom)

$\frac{6.3}{13.8} = \frac{18.9}{x} \\6.3x=(13.8)(18.9)\\6.3x=260.82\\x=41.4$