Question

A guy wire runs from the ground to a cell tower. The wire is attached to the cell tower 150 feet above the ground. The angle formed between the wire and the ground is 48Á (see figure). (Round your answers to one decimal place.)

(a) How long is the guy wire? 201.8 ft

(b) How far from the base of the tower is the guy wire anchored to the ground?
Incorrect: . ft

Answer 1

a. x is the missing value a.sin(48) = 150/x
x = 150/sin(48)
= 202.70 ft

b. tan(48) = 150/x
x = 150/tan(48)
x = 135.13 ft
Remember SOH CAH TOA
sin = opposite/hypothenuse
cos = adjacent/hypothenuse
tan = opposite/adjacent

Answer 2

Explanation:

(A)From the figure drawn, It is given that AB is the height of the cell tower that is equal to=150 feet and the angle formed between the wire and the ground is ∠C=48°.

Then, the length of the guy wire will be:

`(AB)/(AC)=sin48^(\circ)`

⇒
`(150)/(AC)=0.743`

⇒
`AC=(150)/(0.743)`

⇒
`AC=201.8 feet`

thus, the length of the guy wire is 201.8 feet.

(B) The distance of the guy wire from the base of the tower is given s:

`(AB)/(BC)=tan48^(\circ)`

⇒
`(150)/(BC)=1.110`

⇒
`BC=(150)/(1.110)`

⇒
`BC=135.1ft`

Thus, The distance of the guy wire from the base of the tower is 135.1 feet.