Question

A hydro pole casts a shadow that is 10 m long along the ground. A technician measures the wire that runs from the top of the pole to the end of the shadow and finds it to be 26 m. How tall is the pole?

a) 24 m
b) 25 m
c) 28 m
d) 30 m

Answer 1

To find the height of the pole, we use the Pythagorean theorem with the given wire length and shadow length. The calculation reveals that the height of the pole is 24 meters.

Step-by-step explanation:

To determine how tall the pole is, we can use the Pythagorean theorem because the pole, its shadow, and the wire create a right triangle. The square of the length of the wire is equal to the square of the height of the pole (which we want to find) plus the square of the length of the shadow. Let's denote the height of the pole as h.

According to the Pythagorean theorem:

1. Wire length2 = Pole height2 + Shadow length2
2. 262 = h2 + 102
3. 676 = h2 + 100
4. h2 = 676 - 100
5. h2 = 576
6. h = √576
7. h = 24 m

Therefore, the height of the pole is 24 meters, which corresponds to option (a).