Question

14.
If a tree cast a 90-foot shadow at the same time a
3-foot pole held perpendicular to the ground casts
a 5-foot shadow, what is the height of the tree,
expressed in feet?

Answer 1

Answer:

54 feet

Step-by-step explanation:

these are 2 similar right triangles. so the proportions of the sides are equal.

3/5 = x/90

cross multiply to obtain

270 = 5x

divide by 5

54 = x

Answer 2

The height of the tree is 54 ft.

Let the height of the tree is = x feet.

We equate the ratios of the height to shadow.

$\frac{x}{90}=\frac{3}{5}\\ x=\frac{3}{5}\cdot90=54$

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