Question

A 70-foot wire attached to the top of a building is anchored to the ground 20 feet from the base of the building. Which value is the closest to the angle, in radians, that the wire makes with the ground?

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Answer 1

1.28 just took a test

Explanation:

Answer 2

The the angle which the wire make with the ground is 1.280 radian .

Explanation:

Given as :

The length of the wire attached to the top of building = OB = 70 foot

The distance of wire anchored from base of ground = OA = 20 feet

Let the angle made by wire en and ground = Ф

Now from , In Triangle AOB

Cos angle =
`(\textrm Base)/(\textrm Hypotenuse)`

Or, Cos Ф =
`(\textrm OA)/(\textrm OB)`

or, Cos Ф =
`(\textrm 20)/(\textrm 70)`

Or, Cos Ф =
`(\textrm 2)/(\textrm 7)`

∴ Ф =
`Cos^(-1)((2)/(7))`

I.e Ф = 73.39°

Now in radian ,

∵ 180° =
`\pi` radian

∴ 73.39° =
`(\pi )/(180)` × 73.39°

=
`(3.14 )/(180)` × 73.39° = 1.280 radian

Hence The the angle which the wire make with the ground is 1.280 radian . Answer