Question

A rope tied from a tent pole to a take in the ground forms 55 degrees angle with the ground. The pole is 3 feet from the stake, what is the length of the rope to the nearest tenth of a foot

Answer 1

To find the length of the rope, we can use the sine function. In this case, the angle given is 55 degrees and the distance between the pole and the stake is 3 feet. Plugging in the values, we find that the length of the rope to the nearest tenth of a foot is 3.66 feet.

Step-by-step explanation:

To find the length of the rope, we can use the sine function. In this case, the angle given is 55 degrees and the distance between the pole and the stake is 3 feet. We can set up the equation sin(55) = opposite / hypotenuse, where the hypotenuse is the length of the rope. Rearranging the equation, we have hypotenuse = opposite / sin(55).

Plugging in the values, we get hypotenuse = 3 / sin(55). Using a calculator, we find that sin(55) is approximately 0.8192. Therefore, the length of the rope to the nearest tenth of a foot is 3 / 0.8192 ≈ 3.66 feet.

Answer 2

Given:

A rope tied from a tent pole to a stake in the ground forms 55 degrees angle with the ground.

The pole is 3 feet from the stake.

To find:

The length of the rope to the nearest tenth of a foot.

Solution:

First draw a diagram according to the given information as shown below.

We know that, in a right angled triangle,

`\cos \theta = (Base)/(Hypotenuse)`

In triangle ABC,

`\cos 55^\circ=(BC)/(AC)`

`0.573576=(3)/(AC)`

`AC=(3)/(0.573576)`

`AC=5.23034`

`AC\approx 5.2`

Therefore, the length of the rope is 5.2 foot.