Question

geometry p1 pythagorean theorem
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what is the length of the missing leg? if necessary, round to
the nearest tenth.
b = □□□□ feet
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Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs of the right - triangle. Here, \(c = 9.1\) ft and \(a=8.9\) ft. We need to find \(b\), so \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute values

Substitute \(c = 9.1\) and \(a = 8.9\) into the formula: \(b=\sqrt{9.1^{2}-8.9^{2}}\).
First, calculate \(9.1^{2}=82.81\) and \(8.9^{2}=79.21\).
Then \(c^{2}-a^{2}=82.81 - 79.21=3.6\).

Step3: Calculate the square root

\(b=\sqrt{3.6}\approx1.9\) (rounded to the nearest tenth).

Answer:

\(1.9\)