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

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If the height of the building (above S) is h, and the distance from ST to the building is x, then we have

h/x = tan60°
(h-10)/x = tan 30°

Rearrange things a bit and you have

h cot30° = (h-10) cot60°

Now just solve for h.
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