Answer:
 8.3 ft
Step-by-step explanation:
You want the height of the top of a 13 ft ladder whose base is 10 ft from the side of a house.
Pythagorean theorem
The ladder represents the hypotenuse of a right triangle with legs of 10 ft and the height up the side of the house.
 a² +b² = c² . . . . . . . . Pythagorean relation
 a² +10² = 13² . . . . . . . known values filled in
 a² = 169 -100 = 69 . . . . subtract 10²
 a = √69 ≈ 8.3 . . . . . . . . . . . take the square root
The top of the ladder is about 8.3 feet from the ground.
