Question

find the length of the third side. if necessary, write in simplest radical form.
√51
10
answer attempt 1 out of 3
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Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse and \(a\), \(b\) are the legs. Here, the hypotenuse \(c = 10\) and one leg \(a=\sqrt{51}\), and we need to find the other leg \(b\).

Step2: Apply the Pythagorean theorem

From \(a^{2}+b^{2}=c^{2}\), we can re - arrange it to solve for \(b\): \(b=\sqrt{c^{2}-a^{2}}\). Substitute \(c = 10\) and \(a=\sqrt{51}\) into the formula. First, calculate \(c^{2}=10^{2} = 100\) and \(a^{2}=(\sqrt{51})^{2}=51\). Then \(c^{2}-a^{2}=100 - 51=49\).

Step3: Calculate the square root

Now, \(b=\sqrt{49}=7\).

Answer:

7