Question

You are standing 30 meters from a hot air balloon that is preparing to take

off. The angle of elevation from you to the top of the hot air balloon is 28º. Find the
distance from you to the top of the balloon. (Round to two decimal places)

Answer 1

The distance to the top of the balloon is approximately 33.977 meters

Explanation:

The (horizontal) distance from the hot air balloon from the observer, l = 30 m

The angle of elevation to the top of the balloon, θ = 28°

With the balloon standing upright, the distance to the top of the balloon, d, the height of the balloon, h and the horizontal distance to the balloon, l, form a right triangle, where;

d = The hypotenuse side

l = The leg adjacent to the reference (given) angle,

h = The leg opposite to the given angle, θ

By trigonometric ratios, we have;

`cos\angle X = (Adjacent\ leg \ length)/(Hypotenuse \ length)`

From which we get;

`cos\angle \theta = (l)/(d)`

`cos(28^(\circ)) = (30 \ m)/(d)`

`d = (30 \ m)/(cos(28^(\circ)) ) \approx 33.977 \, m`

The distance to the top of the balloon, d ≈ 33.977 m