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Right triangles and trigonometry SAT question
Math · Geometry and Trigonometry · Medium · Answer it here, explanation included.
A right triangle has legs with lengths of centimeters and centimeters. What is the length of this triangle's hypotenuse, in centimeters?
ExplanationShow
Choice B is correct. The Pythagorean theorem states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse. It's given that the right triangle has legs with lengths of centimeters and centimeters. Let represent the length of this triangle's hypotenuse, in centimeters. Therefore, by the Pythagorean theorem, , or . Taking the positive square root of both sides of this equation yields , or . Therefore, the length of this triangle's hypotenuse, in centimeters, is .
Choice A is incorrect and may result from conceptual or calculation errors.
Choice C is incorrect and may result from conceptual or calculation errors.
Choice D is incorrect. This is the square of the length of the triangle’s hypotenuse.
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