A kite flying in the air has an 11-ft line attached to it. Its line is pulled taut and casts a 10-ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.10?11
Question
A kite flying in the air has an 11-ft line attached to it. Its line is pulled taut and casts a 10-ft shadow. Find the height of the kite. If necessary, round your answer to the nearest tenth.10?11
Solution
The problem can be solved using the concept of similar triangles. The shadow, the height of the kite, and the line form a right triangle. The ratio of the sides of this triangle is the same as the ratio of the sides of any similar triangle.
Here are the steps to solve the problem:
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Identify the sides of the triangle: The line (hypotenuse) is 11 ft, the shadow (adjacent side) is 10 ft, and the height of the kite (opposite side) is what we need to find.
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Set up the ratio using the concept of similar triangles: The ratio of the height of the kite to the shadow is the same as the ratio of the line to the shadow. This can be written as: height/10 = 11/10.
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Solve for the height: Multiply both sides of the equation by 10 to solve for the height: height = 11/10 * 10.
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Simplify: The height of the kite is 11 ft.
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