Joe wants to determine the height of a lighthouse. He placed a mirror on the ground so that when he looked into the mirror, he saw the top of the lighthouse. Joe knows that when he uses the mirror, the angles created on either side of it—namely

Question

Joe wants to determine the height of a lighthouse. He placed a mirror on the ground so that when he looked into the mirror, he saw the top of the lighthouse. Joe knows that when he uses the mirror, the angles created on either side of it—namely <BCA and <DCE—will be congruent. He also knows that the angle he forms with the ground and the angle the lighthouse forms with the ground are both right angles.

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Find the height of the lighthouse if Joe’s eyes are 6 feet off the ground, the mirror is placed 56 feet away from the base of the light