Answer:
2.2 (rounded)
Step-by-step explanation:
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}](https://tex.z-dn.net/?f=%5Ccos%20%5Ctheta%20%3D%20%5Cdfrac%7BBase%7D%7BHypotenuse%7D)
In triangle ABC,
![\cos 55^\circ=\dfrac{BC}{AC}](https://tex.z-dn.net/?f=%5Ccos%2055%5E%5Ccirc%3D%5Cdfrac%7BBC%7D%7BAC%7D)
![0.573576=\dfrac{3}{AC}](https://tex.z-dn.net/?f=0.573576%3D%5Cdfrac%7B3%7D%7BAC%7D)
![AC=\dfrac{3}{0.573576}](https://tex.z-dn.net/?f=AC%3D%5Cdfrac%7B3%7D%7B0.573576%7D)
![AC=5.23034](https://tex.z-dn.net/?f=AC%3D5.23034)
![AC\approx 5.2](https://tex.z-dn.net/?f=AC%5Capprox%205.2)
Therefore, the length of the rope is 5.2 foot.
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