By definition, an Isosceles triangle is a triangle that have two congruent sides, and the altitude divides the triangle into two equal Right triangles.
Remember that a Right triangle is a triangle that has an angle whose measure is 90 degrees.
Based on this, you know that:
[tex]\begin{gathered} AD=BD=\frac{AB}{2} \\ \\ AC=BC \end{gathered}[/tex]
Knowing that:
[tex]\begin{gathered} AB=30 \\ AC=17 \end{gathered}[/tex]
You get that:
[tex]\begin{gathered} AD=BD=\frac{30}{2}=15 \\ \\ AC=BC=17 \end{gathered}[/tex]
The Pythagorean Theorem states that:
[tex]a^2=b^2+c^2[/tex]
Where "a" is the hypotenuse and "b" and "c" are the legs of the right triangle.
So you can identify that, for this case:
[tex]\begin{gathered} a=17 \\ b=15 \\ c=CD \end{gathered}[/tex]
Where "CD" is the altitude of the triangle.
Therefore, substituting values and solving for "CD", you get this result:
[tex]\begin{gathered} 17^2=15^2+CD^2 \\ \sqrt[]{17^2-15^2}=CD \\ CD=8 \end{gathered}[/tex]
The answer is: Option (1)
