A person standing on the bank of a river observes that the angle of elevation of the top of a tower on the opposite bank is $60^{\circ}$. When he moves 30 m away from the bank, he finds the angle of elevation to be $30^{\circ}$. Find the height of the tower and width of the river. (Take $\sqrt{3}=1.732$ )
Explanation
Let's assume the height of the tower is h and the width of the river is w. We are given that the angle of elevation of the top of the tower from the bank of the river is 60°, and when the person moves 30 m away from the bank, the angle of elevation becomes 30°. We can use trigonometric ratios to set up two equations: tan 60° = h/w and tan 30° = h/(w + 30). Solving these equations, we get h = 30√3 and w = 10√3.
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