Question

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what is the length of the hypotenuse? if necessary, round to the nearest tenth.
c = \boxed{} feet

Explanation:

Step1: Identify the formula

For a right triangle, the Pythagorean theorem is \( a^2 + b^2 = c^2 \), where \( a \) and \( b \) are the legs, and \( c \) is the hypotenuse. Here, \( a = 84 \) ft and \( b = 35 \) ft.

Step2: Substitute values

Substitute \( a = 84 \) and \( b = 35 \) into the formula: \( 84^2 + 35^2 = c^2 \). Calculate \( 84^2 = 7056 \) and \( 35^2 = 1225 \). Then \( 7056 + 1225 = c^2 \), so \( 8281 = c^2 \).

Step3: Solve for c

Take the square root of both sides: \( c = \sqrt{8281} \). Calculate \( \sqrt{8281} = 91 \).

Answer:

91