Answer to Question #99954 in Geometry for Kamryn

Question

A 6-foot y’all tent casts a 9-foot shadow. If the tent is next to a cardboard box and the box casts a 6-foot long shadow, how tall is the box?

Answer 1

Let us say the height of cardboard box is h feet

and the angle of elevation = $\theta$

$\tan\theta$ = $\frac{Height\thinspace of\thinspace the\thinspace tent }{Length\thinspace of\thinspace tent's\thinspace shadow}$ = $\frac{Height\thinspace of\thinspace the\thinspace box }{Length\thinspace of\thinspace box's\thinspace shadow}$

$\implies$ $\frac{6 }{9}$ = $\frac{h }{6}$

$9h$ = $36$

So $h=4$ feet

Answer: the height of the cardboard box is 4 feet.