Question

A cable 19 m long runs from the top of a utility pole to a point on the ground 10 m from the base of the pole. How tall is the utility pole, to the nearest tenth

Answer 1

Answer:

16.2 m

Step-by-step explanation:

First, we can draw a picture. The cable goes from the top of the pole to the ground (with the pole on the right in my drawing), and the point on the ground is 10 m away from the base of the pole. This forms a right triangle, with the right angle being between the 10 m distance and the pole itself. We can then apply the Pythagorean Theorem, so

a²+b²=c², with c being the side opposite the right angle (the cable), getting us

10²+(length of pole)² = 19²

19²-10²=(length of pole)²

= 261

square root both sides to isolate the length of the pole

length of pole ≈ 16.2 m