Question

A hot air balloon is tethered to a 100-meter rope with no slack. The balloon is 70 meters above the ground. What is the angle of elevation? (to the nearest tenth) A) 34.9° B) 43.5° C) 44.4° D) 45.6°

Answer 1

Draw the situation.

Apply sinθ
`= (opposite)/(hypotenuse)`

sinθ
`=(70)/(100)`

θ =
`sin^(-1)`
`((70)/(100) )`

θ = 44.4°

Answer 2

The value of angle of elevation is 44.4° .

Explanation:

Given as :

The measure of the rope of hot air balloon = 100 m

The height of balloon above the ground = 70 m

Let The angle of elevation = Ф

Now, According to question

Sin angle =
`(\textrm Perpendicular)/(\textrm Hypotenuse)`

Or, SinФ =
`(\textrm Height of baoolon above ground)/(\textrm measure of rope)`

Or, SinФ =
`(70)/(100)`

Or, SinФ =
`(7)/(10)`

∴ Ф =
`Sin^(-1)`(
`(7)/(10)`)

I.e Ф = 44.4°

Hence The value of angle of elevation is 44.4° . Answer