Question

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

Answer 1

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.

$\text{cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}$

$\text{cos}(21^{\circ})=\frac{x}{20}$

$20\cdot \text{cos}(21^{\circ})=\frac{x}{20}\cdot 20$

$x=20\cdot \text{cos}(21^{\circ})$

$x=20\cdot(0.933580426497)$

$x=18.67160852994$

Upon rounding to nearest tenth, we will get:

$x\approx 18.7$

Therefore, the stake is anchoring approximately 18.7 feet away from the base of the tree.