A repairman needs to climb to the top of a building. He takes the measurements shown.The right triangles created by each object and its shadow are similar. Can he use a ladder that reaches heights of up to 28 feet?
To determine if the repairman can use a ladder that reaches heights of up to 28 feet, we need to compare the heights of the repairman and the building.
Let's call the height of the ladder "x".
In the first triangle, we can see that the height of the repairman is 12 feet and the height of the building is 36 feet. The ratio of the height of the repairman to the height of the building is 12/36 = 1/3.
In the second triangle, the height of the repairman is unknown, and the height of the building is also unknown. However, we know that the height of the repairman is 1/3 of the height of the building. So, if we let the height of the building be "y", the height of the repairman would be (1/3)y.
Since the height of the ladder is the sum of the heights of the repairman and the building, we have:
x = (1/3)y + y
Simplifying this equation:
x = (4/3)y
To determine if the repairman can use a ladder that reaches heights of up to 28 feet, we can substitute x = 28 into the equation:
28 = (4/3)y
Multiplying both sides by 3/4:
28 * 3/4 = y
21 = y
Therefore, the height of the building is 21 feet.
Since the height of the building is 21 feet, which is less than the maximum height the ladder can reach (28 feet), the repairman can use a ladder that reaches heights of up to 28 feet.