Question

A 10 foot pole is supporting a temt and has a rope attached to the top. the rope is pulled straight and the other end is attached to the peg two foot above the ground. The rope and the pole form an angle that measures 40 degrees as shown below. which expression shows the length of the rope?

Answer 1

The length of the rope is approximately 8.391 feet.

To find the length of the rope, you can use trigonometry, specifically the tangent function. In the given scenario, the pole, the rope, and the ground form a right-angled triangle. The angle between the pole and the rope is given as 40 degrees. Let's denote the length of the rope as
`\( r \)`.

The tangent of an angle in a right-angled triangle is the ratio of the length of the opposite side to the length of the adjacent side. In this case, the length of the pole is the adjacent side, and the length of the rope is the opposite side.

The tangent of the angle is given by:

`\[ \tan(40^\circ) = \frac{\text{Opposite side}}{\text{Adjacent side}} \]`

Substitute the values:

`\[ \tan(40^\circ) = (r)/(10) \]`

Now, solve for
`\( r \)`:

`\[ r = 10 \tan(40^\circ) \]`

Calculating this expression will give you the length of the rope. Approximating the result, you get:

`\[ r \approx 10 * 0.8391 \approx 8.391 \]`