Trig question?

Question

From a hot air balloon 0.8 km high, a command post is seen with an angle of depression of 12 degrees. how far is it from the point on the ground below the balloon to the command post?

1.3 km
3.8 km
0.8 km
0.2 km

Answer 1

From the given data draw a geometric diagram.

Where, AB = height of the ballon = 0.8 km,

Angle C = depression angle = 12⁰ .

Let, BC = x.

To find x, use the trigonometric function.

Trigonometric function : tan x = opposite side / adjacent side.

tan 12⁰ = AB/x

0.21255 = 0.8/x

⇒ x = 0.8 / 0.21255 = 3.7638 km.

Therefore, the distance from the point on the ground below the ballon to the command post is 3.7638 km.

Option 2 is correct