Question

a guy wire for a tree is 20 ft long, making a 21 angle with the ground. How far is the base of the tree from a stake anchoring the wire?

Answer 1

Answer:

18.7 feet far

Step-by-step explanation:

Based on the information given we can conclude that our set up will be a Right triangle (i.e. one angle is 90°), where the hypotenuse will be denoted by the guy wire of $20ft$  and angle of 21° is the angle formed between then hypotenuse and the base (i.e. ground).

Thus we want to find the base length (lets call it $x$ ) of this triangle, so we can use trigonometry as we have one angle and the hypotenuse, as follow:

$cos(21)=\frac{adjacent side}{hypotenuse}=\frac{baselength}{guywire}\\\\ cos(21)=\frac{x}{20} \\x=20cos(21)\\x=18.671\\x=18.7ft$

So the base is approximately 18.7 feet far from the tree of the anchored wire.