Final answer:
Sara's brother is 18 feet off the ground, as the 45° angled ladder forms an isosceles right triangle with the height equal to the base length, which is 18 feet.
Step-by-step explanation:
The question is asking us to find out how high off the ground Sara's brother is when he is at the top of a ladder angled at 45° with the ground and whose base is 18 feet away from Sara. A ladder leaning against a wall at a 45° angle means that the ladder creates an isosceles right triangle with the ground and the wall. Therefore, the height of the ladder off the ground is equal to the distance from the base of the ladder to Sara, which is 18 feet.
Since the ladder makes a 45° angle with the ground, the ladder is equal in length to the distance from its base to the wall, according to the properties of an isosceles right triangle (1:1:√2 ratio). Sara's brother is 18 feet off the ground if he is at the top of the ladder.