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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)

Respuesta :

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:

[tex]\frac{h_{Elijah}}{s_{Elijah}}=\frac{H_{tree}}{S_{tree}}[/tex]

Replacing terms:

[tex]\frac{1.75}{2.4}=\frac{H}{6.2}[/tex]

Switching sides:

[tex]\frac{H}{6.2}=\frac{1.75}{2.4}[/tex]

Multiplying both sides by 6.2:

[tex]H=6.2\cdot\frac{1.75}{2.4}[/tex]

Simplifying the fractions:

[tex]H=6.2\cdot0.73[/tex]

Multiplying numbers:

[tex]H=4.52\text{ m}[/tex]

The height of the tree is 4.53 meters.

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