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

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,

$\cos \theta = \dfrac{Base}{Hypotenuse}$

In triangle ABC,

$\cos 55^\circ=\dfrac{BC}{AC}$

$0.573576=\dfrac{3}{AC}$

$AC=\dfrac{3}{0.573576}$

$AC=5.23034$

$AC\approx 5.2$

Therefore, the length of the rope is 5.2 foot.