Question

A 20 meter long cable is used to support a telephone pole, holding it perpendicular to the ground. If the cable forms a 60 degree angle with the ground, how high up the pole should the cable be attached? Use the sketchpad to draw a picture.
34.6 meters
28.3 meters
17.3 meters
10 meters

Answer 1

To solve the problem, we'll use some trigonometry. Given that the cable is 20 meters long and forms a 60-degree angle with the ground, we can find the height at which the cable is attached to the pole by using the sine function. The sine of an angle in a right triangle is defined as the opposite side divided by the hypotenuse.

1. Let \( h \) be the height we want to find.
2. The length of the cable is the hypotenuse of the triangle formed by the pole, the ground, and the cable (20 meters).
3. The angle with the ground is 60 degrees.

Using the sine function:

\[
\sin(60^\circ) = \frac{h}{20}
\]

We know that \( \sin(60^\circ) = \frac{\sqrt{3}}{2} \) (approximately 0.866). Therefore:

\[
\frac{\sqrt{3}}{2} = \frac{h}{20}
\]

Multiplying both sides by 20:

\[
h = 20 \times \frac{\sqrt{3}}{2} = 10\sqrt{3}
\]

Using the approximation \( \sqrt{3} \approx 1.732 \):

\[
h \approx 10 \times 1.732 = 17.32 \text{ meters}
\]

So, the height at which the cable should be attached to the pole is approximately 17.3 meters.

**Final Answer: 17.3 meters**.