Solve the problem. If necessary, round to the nearest tenth.
-On a sunny day, a tree and its shadow form the sides of a right triangle. If the hypotenuse is 40 m long and the tree is 32 m tall, how long is the shadow?
A) 51 m
B) 64 m
C) 24 m
D) 72 m

Question

Quizplus · Accepted Answer

To find the length of the shadow, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). If we let the length of the shadow be $b$ and the height of the tree be $a$, then we have $a^2 + b^2 = c^2$. Plugging in the given values, $32^2 + b^2 = 40^2$. Solving for $b$, we find $b = \sqrt{40^2 - 32^2} = \sqrt{1600 - 1024} = \sqrt{576} = 24$. Therefore, the length of the shadow is 24 m.

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