Find the length of the altitude to the base of an isosceles triangle if the length of one leg is 17 and the base is 16.

8^2 + h^2 = 17^2

To find the length of the altitude to the base of an isosceles triangle, we can apply the Pythagorean theorem.

Step 1: Draw the isosceles triangle.

Step 2: Label the two congruent legs as 'a' and the base as 'b'. In this case, one leg is given as 17, so we have a = 17, and the base is given as 16, so b = 16.

Step 3: Since it is an isosceles triangle, we know that the altitude from the apex to the base bisects the base, dividing it into two equal segments. Therefore, the base is divided into two segments of length b/2 = 16/2 = 8.

Step 4: Label the altitude as 'h'.

Step 5: Apply the Pythagorean theorem: a² = h² + (b/2)².

Substituting the given values, we have 17² = h² + 8².

Step 6: Simplify the equation: 289 = h² + 64.

Step 7: Solve for h: Subtract 64 from both sides:

289 - 64 = h².

225 = h².

Step 8: Take the square root of both sides: √(225) = √(h²).

15 = h.

Therefore, the length of the altitude to the base of the isosceles triangle is 15.