When viewing Angel Falls (the world's highest waterfall) from Observation Platform A, located on the

same level as the bottom of the waterfall, we calculate the angle of elevation to the top of the waterfall to
be 69.30°. From Observation Platform B, which is located on the same level exactly 1000 feet from the
first observation point, we calculate the angle of elevation to the top of the waterfall to be 52.90°. How
high is the waterfall?

You are obviously looking at or have made a diagram.

let the top of the falls be point C
In triangle ABC
B = 52.9°
A = 110.7° , the supplement of 69.3
then angle C = 16.4°
by the Sine law
AC/sin52.9 = 1000/sin16.4
AC = 2824.8913...

now in the right-angled triangle
sin69.3 = height/2824.8913..
height = 2642.5 feet

To find the height of the waterfall, we can use trigonometry and the information provided about the angles of elevation and the distance between the observation platforms.

Let's denote the height of the waterfall as 'h.'

From Observation Platform A, we have an angle of elevation of 69.30°. This means that the tangent of the angle is equal to the height of the waterfall divided by the distance from the observation platform to the base of the waterfall. In this case, the distance is 0 because both the observation platform and the base of the waterfall are on the same level.

So, we have the equation:

tan(69.30°) = h / 0

Since we can't divide by 0, this equation doesn't provide any meaningful information. However, we can still use the second observation point to solve for the height of the waterfall.

From Observation Platform B, we have an angle of elevation of 52.90°. Here, the distance between the observation platform and the base of the waterfall is given as 1000 feet.

Using the same logic as before, we have the equation:

tan(52.90°) = h / 1000

To find the height of the waterfall, we can rearrange the equation:

h = 1000 * tan(52.90°)

Solving this equation gives us the height of the waterfall.