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

Answer:

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

Step-by-step 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 = $\dfrac{\textrm base}{\textrm hypotenuse}$

I.e cosФ = $\dfrac{\textrm OA}{\textrm OB}$

Or, cosФ = $\dfrac{\textrm x}{\textrm h}$

Or, cosФ = $\dfrac{\textrm 260 meters}{\textrm 340 meters}$

Or, cosФ = $\dfrac{\textrm 13}{\textrm 17}$

∴ Ф = $cos^{-1}(\frac{13}{17})$

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