Question

The shadow of a vertical pole on level ground is 10 ft. more than one-third the height of the pole. If the shadow is 19 ft. long, how high is the pole?

Answer 1

The height of the vertical pole is 27 feet, determined by setting up an equation using the given information about the relationship between the pole's height and its shadow length.

Step-by-step explanation:

The student is asking about the height of a vertical pole given that the shadow of the vertical pole is 10 ft. more than one-third the height of the pole and that the shadow is 19 ft. long. To find out how high the pole is, we can set up the following equation based on the information given:

Let h represent the height of the pole. According to the problem, the shadow is one-third the height of the pole plus an additional 10 ft., and we know the shadow is 19 ft. long. Therefore, the relationship between the shadow's length and the pole's height can be written as:

1/3h + 10 ft = 19 ft

To solve for h, we first move the 10 ft to the other side of the equation:

1/3h = 19 ft - 10 ft

1/3h = 9 ft

Then we multiply both sides by 3 to isolate h:

h = 9 ft × 3

h = 27 ft

Therefore, the pole is 27 feet tall.