Question

A 20 foot cable is attached to the ground from the top of a telephone pole. If it reaches the ground 13 feet from the base of the pole, what is the angle created between the ground and the cable?

Answer 1

Ответ:

60.87 degrees

Объяснение:

To find the angle created between the ground and the cable, we can use the Pythagorean theorem. Let's call the angle "x". Then, we have:

20^2 = 13^2 + (20 * sin(x))^2

Expanding the right side of the equation and solving for sin(x), we get:

sin(x) = sqrt(400 - 169) / 20

Taking the inverse sine (arcsin) of both sides, we get:

x = asin(sqrt(231) / 20)

Finally, converting from radians to degrees:

x = asin(sqrt(231) / 20) * 180 / pi

x = approximately 60.87 degrees.

So the angle created between the ground and the cable is approximately 60.87 degrees.

Answer 2

To find the angle created between the ground and the cable, you can use trigonometry, specifically the tangent function.

In this scenario, the telephone pole, the cable, and the ground form a right triangle. The telephone pole represents the height (opposite side), the cable represents the hypotenuse, and the distance from the base of the pole to the point where the cable touches the ground represents the adjacent side.

You have the following information:

• The height of the telephone pole (opposite side) is 20 feet.
• The distance from the base of the pole to where the cable touches the ground (adjacent side) is 13 feet.

Now, you can use the tangent function:

$\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$

Substitute the values you have:

$\tan(\theta) = \frac{20}{13}$

Now, you want to find the angle ($\theta$). To do this, you'll take the inverse tangent (arctan) of both sides:

$\theta = \arctan\left(\frac{20}{13}\right)$

Use a calculator to find the arctan of $\frac{20}{13}$:

$\theta \approx 55.62^\circ$

So, the angle between the ground and the cable is approximately 55.62 degrees.