Question

Elijah is 1.75 meters tall, and casts a 2.4 meter shadow. He sees that the head of his shadow lines up with the top of a nearby tree's shadow. He is 6.2 meters away from the tree. How tall is the tree? (Round to the nearest hundredth if needed)

Answer 1

EXPLANATION

Let's see the facts:

Tall=height=h 1.75m

Shadow=s= 2.4 m

Distance from the tree= shadow of the tree= 6.2 meters

We can apply the trigonometric relationship as shown as follows:

`(h_(Elijah))/(s_(Elijah))=(H_(tree))/(S_(tree))`

Replacing terms:

`(1.75)/(2.4)=(H)/(6.2)`

Switching sides:

`(H)/(6.2)=(1.75)/(2.4)`

Multiplying both sides by 6.2:

`H=6.2\cdot(1.75)/(2.4)`

Simplifying the fractions:

`H=6.2\cdot0.73`

Multiplying numbers:

`H=4.52\text{ m}`

The height of the tree is 4.53 meters.