A15-foot telephone pole has a wire that extends from the top of the pole to the ground. the wire and the ground form a 42 degree angle. how long is the wire, and what is the distance from the base of the pole to the spot where the wire touches the ground.

The length of the wire is 22.42 feet

The distance from the base of the pole to the spot where the wire touches the ground is 16.66 feet

Step-by-step explanation:

* Lets explain the situation in the problem

- The telephone pole , the wire and the ground formed a right triangle

- The wire is the hypotenuse of the triangle

- The height of the telephone pole and the distance from the base of

 the pole to the spot where the wire touches the ground are the legs

 of the triangle

- The angle between the wire and the ground is 42°

- The angle 42° is opposite to the height of the telephone pole

- The height of the telephone pole is 15 feet

* Lets use the trigonometry functions to find the length of the wire

 (hypotenuse) and the distance from the base of the pole to the spot

 where the wire touches the ground

∵ sin Ф = opposite/hypotenuse

∵ Ф = 42° and its opposite side = 15 feet

∴ sin 42 = 15/hypotenuse ⇒ by using cross multiplication

∴ sin 42° (hypotenuse) = 15 ⇒ divide both sides by sin 42

∴ hypotenuse = 15/sin 42° = 22.42 feet

∵ The length of the wire is the hypotenuse

∴ The length of the wire is 22.42 feet

∵ The distance from the base of the pole to the spot where the wire

   touches the ground is the adjacent side to the angle 42°

∵ tan Ф = opposite/adjacent

∴ tan 42° = 15/adjacent ⇒ by using cross multiplication

∴ tan 42° (adjacent) = 15 ⇒ divide both sides by sin 42

∴ adjacent = 15/tan 42° = 16.66 feet

∵ The adjacent side is the distance from the base of the pole to the

  spot where the wire touches the ground

∴ The distance from the base of the pole to the spot where the wire

   touches the ground is 16.66 feet

answer: the answer is one of

step-by-step explanation:   we are given to write a proper fraction where the whole is divided into an even number of equal parts less than ten, and an odd number of those parts exist.

an even number less than 10 may be one of 2, 4, 6 or 8. so, the whole may be one of these four evens.

now, an odd number of these parts must exist, so the numerator must be an odd number, one of 1, 3, 5 or 7. it cannot be 9 because then the fraction will become improper.

thus, our fraction may be one of the following

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}