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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.)

Respuesta :

ajeigbeibraheem

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;

[tex]\overline {BC}[/tex] to be the height of the tree and [tex]\overline {DE}[/tex] 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

[tex]\dfrac{\overline {DE}}{ \overline {BC}}= \dfrac{\overline{AD}}{ \overline{AC}}[/tex]

[tex]\dfrac{x}{ 45}= \dfrac{225-220}{225}[/tex]

[tex]\dfrac{x}{ 45}= \dfrac{25}{225}[/tex]

By cross multiply

225x = 45 × 25

[tex]x = \dfrac{45 \times 25}{225}[/tex]

[tex]x = \dfrac{1125}{225}[/tex]

x = 5.0 ft

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

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