Question

cSuppose you are standing such that a 45-foot tree is directly between you and the sun. If you are standing 200 feet away from the tree and the tree casts a 225-foot shadow, how tall could you be and still be completely in the shadow of the tree? x 225 ft 200 ft 45 ft Your height is ft (If needed, round to 1 decimal place.)

Answer 1

you could stand at 5.0 ft and still be completely in the shadow of the tree

Explanation:

From the diagram attached below;

We consider;

`\overline {BC}` to be the height of the tree and
`\overline {DE}` to be the height of how tall you could be and still be completely in the shadow of the tree.

∠D = ∠B = 90°

Also;

ΔEAD = ΔBAC (similar triangles)

Therefore, their sides will also be proportional

i.e

`\frac{\overline {DE}}{ \overline {BC}}= \frac{\overline{AD}}{ \overline{AC}}`

`(x)/( 45)= (225-220)/(225)`

`(x)/( 45)= (25)/(225)`

By cross multiply

225x = 45 × 25

`x = (45 * 25)/(225)`

`x = (1125)/(225)`

x = 5.0 ft

Therefore, you could stand at 5.0 ft and still be completely in the shadow of the tree