A right triangle is given with the lengths of a leg and the hypotenuse.
It is required to find the missing side.
The Pythagorean Theorem states that in a right triangle, the relationship between the lengths of legs a and b, and the length of the hypotenuse c is:
[tex]a^2+b^2=c^2[/tex]
Let the length of the missing side be a.
Substitute b=15 and c=17 into the equation:
[tex]a^2+15^2=17^2[/tex]
Solve the resulting equation for a:
[tex]\begin{gathered} a^2+15^2=17^2 \\ \text{ Evaluate the squares:} \\ \Rightarrow a^2+225=289 \\ \text{ Subtract }225\text{ from both sides:} \\ \Rightarrow a^2+225-225=289-225 \\ \Rightarrow a^2=64 \\ \text{ Take the square root of both sides:} \\ \Rightarrow\sqrt{a^2}=\sqrt{64} \\ \Rightarrow a=8 \end{gathered}[/tex]
Hence, the length of the missing side is 8.
The answer is 8.
