The angles of elevation of the highest point of a building from two points S and T are 60 degree and 30 degree respectively,T is vertically above S and ST=10m.Calculate the height of the building above the level of S
Draw a diagram. It should be clear that
h cot60° = (h-10) cot30°
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To solve this problem, we can use trigonometry and create a right triangle.
Let's consider the triangle STB, where ST is the base, TB is the height of the building, and angle T is 60°. We can use the tangent function to find the height of the building.
tan(T) = TB / ST
tan(60°) = TB / 10m
√3 = TB / 10m
TB = 10m * √3
So, the height of the building above the level of S is 10√3 meters.