A and B are two balloons at the same height and 1000m apart. O is ground observation position,angle AOX =14°15' and angle BOX=10°30'.Find the height of the balloons

3 answers

Let the height of the balloons be x meters.

In triangle AOX,
tan(14°15') = x/1000

In triangle BOX,
tan(10°30') = x/1000

Now, solve for x in both equations:

tan(14°15') = x/1000
x = 1000 * tan(14°15')

x ≈ 243.89 meters

Therefore, the height of the balloons is approximately 243.89 meters.
where is X?
On the ground? On the line AB?
I apologize for the confusion. Let's correct the solution.

Let's consider the triangle AOB with side lengths as 1000m (AB), height of the balloons (h), and the distance of the observer position O from line AB. Let's say the distance of O from line AB is d meters.

In triangle AOX, tan(14°15') = h/d
In triangle BOX, tan(10°30') = h/(1000 - d)

We know that the observer is ground observation positioned at O. So, the distance of O from line AB is 0 (d=0).

Let's substitute the values in the equation:

tan(14°15') = h/0 => h=0

This means that the height of the balloons is 0 meters, and the observer is directly below the line joining the two balloons.