Question

A hot air balloon is 2,750 feet above the ground. The angle of depression from the basket of the balloon to the base of the silo is 42 degrees. Set up, but DO NOT solve an equation that would be used to find the distance from the basket to the base of the silo. **Must provide an explanation to go with your equation. Do not solve your equation!

Answer 1

d = 2750 ÷ sin 42°

d = [2750/(sin 42°)]

We're told not to solve the equation.

Explanation:

From the attached image

The angle of elevation of the basket from the base of the silo = the angle of depression of the base of the silo from the basket of the hot air ballon = 42° (alternate angles are equal)

So, from here, trigonometric relations can then be used to calculate the distance from the basket to the base of the silo

Sin θ = (Opp/Hyp)

θ = 42°, Opp = 2750 ft, Hyp = d

Sin 42° = (2750/d)

d = 2750 ÷ sin 42°

d = [2750/(sin 42°)]

Hope this Helps!!!

Answer 2

d = 2750/Cos 48

Explanation:

We need the value of the angle from the vertical axis

90 - 42 = 48°

We are trying to find the distance d which is the Hypotenuse of the right angled triangle formed.

The relationship between the adjacent and hypotenuse is help by the cosine of the angle between them

such that

Cos 48 = Adj/Hyp

Cos 48 = 2750/d

d Cos 48 = 2750

d = 2750/Cos 48