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,
[tex]\cos \theta = \dfrac{Base}{Hypotenuse}[/tex]
In triangle ABC,
[tex]\cos 55^\circ=\dfrac{BC}{AC}[/tex]
[tex]0.573576=\dfrac{3}{AC}[/tex]
[tex]AC=\dfrac{3}{0.573576}[/tex]
[tex]AC=5.23034[/tex]
[tex]AC\approx 5.2[/tex]
Therefore, the length of the rope is 5.2 foot.