A woman 5ft 6in tall stands so that the tip of her shadow coincides with the tip of the shadow of a tall tree. The woman stands 18 ft from the tip of her shadow and 100 ft from the base of the tree. How tall is the tree?
h/5.5 = 100/18
A vertical pole 10 meters high casts a shadow 8 meters long. At the same time, a nearby tree casts a
shadow 40 meters long. Find the height of the tree in meters.
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The answer is 36 1/18 ft.
To find the height of the tree, we can set up a proportion using the similar triangles formed by the woman and her shadow, and the tree and its shadow.
First, let's convert the height of the woman from feet and inches to just feet. Since there are 12 inches in a foot, and the woman is 5 feet 6 inches tall, she is 5 + (6 / 12) = 5.5 feet tall.
Now, let's set up the proportion. The height of the woman (5.5 feet) divided by the length of her shadow (18 feet) must be equal to the height of the tree (unknown) divided by the length of the tree's shadow (100 feet).
Therefore, our proportion is:
5.5 / 18 = x / 100
To solve for x (the height of the tree), cross-multiply:
5.5 * 100 = 18 * x
550 = 18x
Divide both sides by 18:
x = 550 / 18
x ≈ 30.56
Therefore, the height of the tree is approximately 30.56 feet.