A person standing at a point $A$ finds the angle of elevation of a nearby tower to be $60^{\circ}$. From A, the person walks a distance of $100 ft$ to a point $B$
and then walks again to another point $C$ such that $\angle ABC=120^{\circ}$. If the angles of elevation of the tower at both $B$ and $C$ are also $60^{\circ}$ each, then what is the height of the tower?
Here, I have found that the tower will be at the circumcentre of the triangle. However nothing is said about length of $BC$. Assuming it to be $100 ft$ , I have found out the height of tower is $100\sqrt{3}ft$. However there must be another way of doing it without making the unnecessary assumption.
Best Answer
Turning my comment into an answer, since it appears to be the answer here.
I kind of doubt that there will be a way to avoid that extra assumption. But you can check that yourself: assume some different value for the length $BC$, and if that results in a different height then you know that the problem statement is incomplete or plain wrong.