Question

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

Answer 1

Answer:

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

Step-by-step 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;

$cos\angle X = \dfrac{Adjacent\ leg \ length}{Hypotenuse \ length}$

From which we get;

$cos\angle \theta = \dfrac{l}{d}$

$cos(28^{\circ}) = \dfrac{30 \ m}{d}$

$d = \dfrac{30 \ m}{cos(28^{\circ}) } \approx 33.977 \, m$

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