contestada

Ayden is 1.85 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 39.55 meters. He stands 35.4 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Respuesta :

The height of the tree is 4.15m

We are given that

Height of Joshua, h=1.85 m

Length of tree's shadow, L=39.55 m

Distance between the tree and Joshua=35.4 m

We have to find the height of the tree.

BC=35.4 m

BD=39.55m

What is the height?

CD=BD-BC

CD=-35.4 m=4.15 m

EC=1.45 m

All right triangles are similar. When two triangles are similar then the ratio of their corresponding sides is equal.

[tex]\triangle ABD=\triangle ECD[/tex]

[tex]\frac{AB}{EC}=\frac{BD}{CD}[/tex]

Substitute the values

[tex]\frac{AB}{1.45}=\frac{39.55\times 1.45}{4.15} \\\\AB=20.39[/tex]

Hence, the height of the tree=20.39 m

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