Question

A power line is connecting the top of a building to the ground at the building (angle of depression) if the wire is 340 meters long

Answer 1

The angle of depression of the power line making with ground and connected to the top of building is 40.11° .

Explanation:

Given as :

The length of the wire connected to the top of building = h = 340 meters

The distance of the power line away from base of building = x = 260 meters

Let The angle of depression = Ф

Now, from figure

cos angle =
`(\textrm base)/(\textrm hypotenuse)`

I.e cosФ =
`(\textrm OA)/(\textrm OB)`

Or, cosФ =
`(\textrm x)/(\textrm h)`

Or, cosФ =
`(\textrm 260 meters)/(\textrm 340 meters)`

Or, cosФ =
`(\textrm 13)/(\textrm 17)`

∴ Ф =
`cos^(-1)((13)/(17))`

or, Ф =
`cos^(-1)(0.7647)`

So , Ф = 40.11°

So, The angle of depression from the ground = Ф = 40.11°

Hence, The angle of depression of the power line making with ground and connected to the top of building is 40.11° . Answer