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

Respuesta :

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.

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