The angles of elevation of a hot air balloon from two points, A and B, on level ground, are 24.2 and 46.8 degrees, respectively. The points A and B are 8.4 miles apart, and the balloon is between the points in the same vertical plane. Find the height of the balloon above the ground.

The height of the balloon above the ground is 2.65 miles.

Step-by-step explanation:

Given:

Angle of elevation of balloon from point A (a) = 24.2°

Angle of elevation of balloon from point B (b) = 46.8°

The distance between A and B (AB) = 8.4 miles

Consider two right angled triangles representing the given scenario.

Let the height of balloon be 'H'. So,

From triangle AOC, using cotangent of angle 'a', we have:

From triangle BOC, using cotangent of angle 'b', we have:

Now,

Plug in the values of 'a' and 'b' and solve for 'H'. This gives,

Therefore, the height of the balloon above the ground is 2.65 miles.

people went from manufacturing one object at a time by hand to manufacturing many objects in factories

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x