Question

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100 mm
96 mm
what is the length of the missing leg? if necessary, round to the nearest tenth.
a = millimeters

Explanation:

Step1: Identify the formula

This is a right triangle, so we use the Pythagorean theorem: \( c^2 = a^2 + b^2 \), where \( c \) is the hypotenuse, and \( a, b \) are the legs. Here, \( c = 100 \) mm, \( b = 96 \) mm, and we need to find \( a \). Rearranging the formula: \( a^2 = c^2 - b^2 \).

Step2: Substitute the values

Substitute \( c = 100 \) and \( b = 96 \) into the formula: \( a^2 = 100^2 - 96^2 \). Calculate \( 100^2 = 10000 \) and \( 96^2 = 9216 \). Then \( a^2 = 10000 - 9216 = 784 \).

Step3: Solve for \( a \)

Take the square root of 784: \( a = \sqrt{784} = 28 \).

Answer:

28