Question

The two hot-air balloons in the drawing are 48.2 and 61.0 m above the ground. A person in the left balloon observes that the right balloon is 13.3° above the horizontal. What is the horizontal distance x between the two balloons?

Answer 1

Answer:

x = 54.15 meters between the balloons horizontally.

Explanation:

Hence, vertical distance between balloons is 12.8 meters.

y= 61-48.2  = 12.2 m

A right-angle triangle is formed with,

angle θ = 13.3 degrees

opposite (y) = 12.8

adjacent (x) = ?

$tan\theta = \dfrac{y}{x}$

Now by putting the values in the above equation.

$tan13^{\circ}=\dfrac{12.8}{x}$

$x=\dfrac{12.8}{tan13^{\circ}}$

x = 54.15 meters between the balloons horizontally.