Answer:
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
