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# The angle of elevation of the top of a tower from a point on the ground, which is 30 m away from the foot of the tower, is 30º. Find the height of the tower.

Let AB be the tower of height h metres and let C be a point at a distance of 30 m from the foot of the tower. The angle of elevation of the top of the tower from point C is given as 30º.

In $$∆ \ CAB$$, we have

$$\frac{AB}{CA} \ = \ tan30º$$

$$\frac{h}{30} \ = \ \frac{1}{ \sqrt{3}} \ => \ h \ = \ \frac{30}{ \sqrt{3}} \ = \ 10 \sqrt{3}$$

Hence, the height of the tower is $$10 \sqrt{3}$$ metres.