Question

find the length of the third side. if necessary, round to the nearest tenth.
6
7
answer attempt 2 out of 2
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Explanation:

Step1: Identify the triangle type

The triangle is a right - triangle (has a right - angle symbol). For a right - triangle, we can use the Pythagorean theorem, which states that for a right - triangle with legs of lengths \(a\) and \(b\) and hypotenuse of length \(c\), \(c^{2}=a^{2}+b^{2}\) (or if we are finding a leg, \(a^{2}=c^{2}-b^{2}\), but in this case, the two given sides are the legs since the right angle is between them, and we need to find the hypotenuse). Here, \(a = 6\) and \(b=7\).

Step2: Apply the Pythagorean theorem

Using the formula \(c=\sqrt{a^{2}+b^{2}}\), substitute \(a = 6\) and \(b = 7\) into the formula. First, calculate \(a^{2}\) and \(b^{2}\): \(a^{2}=6^{2}=36\) and \(b^{2}=7^{2}=49\). Then, find the sum of these two values: \(36 + 49=85\). Now, take the square root of 85: \(c=\sqrt{85}\approx9.2\) (rounded to the nearest tenth).

Answer:

\(9.2\)