Answer:
Step-by-step explanation:To find the length of the altitude AD in an isosceles triangle, we can use the Pythagorean Theorem.
Given:
Base BC = 16
Sides AB = AC = 9
Step 1: Draw the altitude AD from vertex A to base BC.
Step 2: Since triangle ABC is isosceles, AD will be the perpendicular bisector of base BC.
Step 3: The length of the altitude AD can be found by using the Pythagorean Theorem in triangle ABD or triangle ACD.
In triangle ABD:
AB² = AD² + BD²
(9)² = AD² + (8)²
81 = AD² + 64
AD² = 81 - 64
AD² = 17
AD = √17
In triangle ACD:
AC² = AD² + CD²
(9)² = AD² + (8)²
81 = AD² + 64
AD² = 81 - 64
AD² = 17
AD = √17
Since both triangle ABD and triangle ACD yield AD = √17, we can conclude that the length of the altitude AD in triangle ABC is √17.