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A 6 ft tall tent standing next to a cardboard box casts a 9 ft shadow. If the cardboard box casts a shadow that is 6 ft long then how tall is it?

Answer 1

Noah Atkinson

Let the cardboard box is #hft# tall and the angle of elevation if source of light be #alpha#

Then

#tanalpha="height of the tent"/"length of its shadow" ="height of the box"/"length of its shadow"#

So #6/9=h/6#

#=>h=6^2/9=4# ft

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Answer 2

Caroline Aucoin

To solve this problem, we'll use similar triangles.

The ratio of the height of the tent to the length of its shadow is the same as the ratio of the height of the cardboard box to the length of its shadow.

So, (height of tent)/(length of tent's shadow) = (height of cardboard box)/(length of cardboard box's shadow).

Substitute the given values: (6 ft)/(9 ft) = (height of cardboard box)/(6 ft).

Cross multiply and solve for the height of the cardboard box: 6 * 6 = 9 * (height of cardboard box) 36 = 9 * (height of cardboard box) Height of cardboard box = 36/9 Height of cardboard box = 4 ft.

Therefore, the cardboard box is 4 ft tall.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.