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Geometry and Trigonometry / Right triangles and trigonometry Difficulty: Easy

The lengths of the legs of a right triangle are shown. Which of the following is closest to the length of the triangle's hypotenuse?

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Explanation

Choice C is correct. The Pythagorean theorem states that for a right triangle, $a^{2} + b^{2} = c^{2}$ , where $a$ and $b$ represent the lengths of the legs of the triangle and $c$ represents the length of its hypotenuse. In the triangle shown, the legs have lengths of $3$ and $7$ . Substituting $3$ for $a$ and $7$ for $b$ in the equation $a^{2} + b^{2} = c^{2}$ yields $3^{2} + 7^{2} = c^{2}$ , which is equivalent to $9 + 49 = c^{2}$ , or $58 equals c squared$ . Taking the positive square root of both sides of this equation yields $StartRoot 58 EndRoot equals c$ . Thus, the value of $c$ is approximately $7.6$ . Therefore, of the given choices, $7.6$ is the closest to the length of the triangle's hypotenuse.

Choice A is incorrect and may result from conceptual or calculation errors.

Choice B is incorrect and may result from conceptual or calculation errors.

Choice D is incorrect and may result from conceptual or calculation errors.