The angles of elevation of the highest point of a building from two points S and T are 60° and 30° respectivelly T is vertically above S and |ST| =10m calculete the height of the bulding above the level of S with solution

If h is the height of the building above S, then we have

h cot30° = (h-10)cot60°

To find the height of the building above the level of point S, we can use trigonometry and the given angles of elevation.

Let's consider the right-angled triangle formed by points S, T, and the top of the building.

In triangle STB, where B represents the top of the building:

1. Mark the angle of elevation from S as 60°. This means that angle STB is 60°.
2. Mark the angle of elevation from T as 30°. This means that angle TBS is 30°.
3. The distance from S to T is given as |ST| = 10m.

Now, we can use the trigonometric ratios of sine and tangent to solve for the height of the building.

First, let's find the length of the opposite side to angle STB (height of the building).
Using the sine function: sin(60°) = opposite / hypotenuse

sin(60°) = b / 10 (where b represents the height of the building)

To solve for b, we rearrange the equation:

b = 10 * sin(60°)
b ≈ 8.66 m

Therefore, the height of the building above the level of point S is approximately 8.66 meters.