Question

the angle of the elevation of the top of the tower observed from each of the three points A B and C on the ground forming a triangle is the same angle Alpha if R is the circumradius of the triangle ABC then the height of the Tower is

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Answer 1

Answer:

Height = Tan (Alpha)*R

Step-by-step explanation:

The only way for the angle of the elevation of the top of a tower to be the same for three points on the ground is for them all to be the same distance from the top of the tower. So the circumradius of the triangle formed by the three points is centered on the tower itself. The circumradius is the distance from the points to the base of the tower.

Using SOH CAH TOA we know that the TAN(Alpha) = Opposite/Adjacent

So Tan(Alpha) = Height/R

Some simple algebra and we get

Tan(Alpha)*R= Height.