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Geometry and Trigonometry Difficulty: Easy

In the right triangle shown, which of the following is closest to the value of $c$ ?

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Explanation

Choice B is correct. By the Pythagorean theorem, if a right triangle has a hypotenuse with length $t$ and legs with lengths $r$ and $s$ , then $r^{2} + s^{2} = t^{2}$ . It's given in the right triangle shown that the legs have lengths of $9$ and $6$ and the hypotenuse has a length of $c$ . Substituting $9$ for $r$ , $6$ for $s$ , and $c$ for $t$ in $r^{2} + s^{2} = t^{2}$ yields $9^{2} + 6^{2} = c^{2}$ , or $117 equals c squared$ . Taking the square root of both sides of this equation yields $\pm \sqrt{117} = c$ . Since the length of a side of a triangle must be positive, the value of $c$ is $StartRoot 117 EndRoot$ , which is approximately equal to $10.8167$ . Of the choices, $10.8$ is the closest to the value of $c$ .

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 and may result from conceptual or calculation errors.