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We need to use the Pythagorean Theorem.

It states that a^2 + b^2= c^2, where a and b are the legs of the right angle triangle and c is the hypotenuse.

13 is the hypotenuse, 7 and b are the legs. 

[tex]7^2 + b^2 = 13^2\\\\49 + b^2 = 169\\\\b^2 = 169 - 49\\\\b^2 = 120\\\\b=\sqrt{120} = \sqrt{4 \cdot 30} = \boxed{\bf{2\sqrt{30}}}[/tex]

The value of b is 2√(30).

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