Question

question
find the length of the third side. if necessary, round to the nearest tenth.
16
18
answer attempt 1 out of 2
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Explanation:

Step1: Identify triangle type

It's a right triangle, so use Pythagorean theorem: \(a^2 + b^2 = c^2\), where \(c\) is hypotenuse, \(a,b\) are legs. Here, one leg \(a = 16\), hypotenuse \(c = 18\), find the other leg \(b\).

Step2: Rearrange formula for \(b\)

From \(a^2 + b^2 = c^2\), get \(b = \sqrt{c^2 - a^2}\).

Step3: Substitute values

\(c = 18\), \(a = 16\), so \(b = \sqrt{18^2 - 16^2}\). Calculate \(18^2 = 324\), \(16^2 = 256\). Then \(324 - 256 = 68\). So \(b = \sqrt{68}\).

Step4: Simplify \(\sqrt{68}\)

\(\sqrt{68} \approx 8.2\) (rounded to nearest tenth).

Answer:

\(8.2\)