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

Answer:

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

Step-by-step 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

$\dfrac{\overline {DE}}{ \overline {BC}}= \dfrac{\overline{AD}}{ \overline{AC}}$

$\dfrac{x}{ 45}= \dfrac{225-220}{225}$

$\dfrac{x}{ 45}= \dfrac{25}{225}$

By cross multiply

225x = 45 × 25

$x = \dfrac{45 \times 25}{225}$

$x = \dfrac{1125}{225}$

x = 5.0 ft

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