Answer:
18.7 feet.
Step-by-step explanation:
Please consider the complete question.
A guy wire for a tree is 20 ft long, making a 21 degree angle with the ground. How far is the base of the tree from a stake anchoring the wire?
First of all, we will draw a relevant diagram to represent the given scenario. Our diagram would be a right triangle with hypotenuse of 20 ft and x as adjacent side to angle 21 degrees as represented in the attachment.
We know that cosine relates opposite side of right triangle with its hypotenuse.
[tex]\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}[/tex]
[tex]\text{cos}(21^{\circ})=\frac{x}{20}[/tex]
[tex]20\cdot \text{cos}(21^{\circ})=\frac{x}{20}\cdot 20[/tex]
[tex]x=20\cdot \text{cos}(21^{\circ})[/tex]
[tex]x=20\cdot(0.933580426497)[/tex]
[tex]x=18.67160852994[/tex]
Upon rounding to nearest tenth, we will get:
[tex]x\approx 18.7[/tex]
Therefore, the stake is anchoring approximately 18.7 feet away from the base of the tree.
