Answer:
[tex]15\; {\rm cm}[/tex].
Step-by-step explanation:
Refer to the diagram attached. Because the triangle is isosceles, the altitude to the base of the triangle would bisect the base. Given that the base is of length [tex]16\; {\rm cm}[/tex], each half of the base would be of length [tex](1/2)\, (16\; {\rm cm}) = 8\; {\rm cm}[/tex].
Each of the two [tex]17\; {\rm cm}[/tex] sides forms a hypotenuse in a right triangle. The two other sides (adjacent to the right angle) would be:
- Half of the base of length [tex]8\; {\rm cm}[/tex], and
- The altitude [tex]h[/tex] to the base, which needs to be found.
Apply Pythagorean Theorem to find the length of the altitude:
[tex]\begin{aligned} h &= \sqrt{(17\; {\rm cm})^{2} - (8\; {\rm cm})^{2}} = 15\; {\rm cm} \end{aligned}[/tex].
In other words, the length of the altitude to the base would be [tex]15\; {\rm cm}[/tex].
