The angle of elevation of the top of a tower from a point 30m away is 30°. Find the height of the tower.

Answer: $10\sqrt{3}$ m. Using 30-60-90 logic: Side opposite to 60° (Base) is $30$. Side opposite to 30° (Height) is $30/\sqrt{3} = 10\sqrt{3}$.

The shadow of a tower is $\sqrt{3}$ times its height. The Sun's elevation is:

Answer: 30°. Height/Shadow = $1/\sqrt{3}$. $\tan \theta = 1/\sqrt{3} \Rightarrow \theta = 30°$.

Learn to solve tower, shadow, and observation problems using trigonometric ratios and angle shortcuts (30-60-90 rule).

Instead of $\tan \theta$ , use side ratios for common triangles:

30-60-90 Triangle: Sides opposite to 30:60:90 are in ratio $1 : \sqrt{3} : 2$ .
45-45-90 Triangle: Sides opposite to 45:45:90 are in ratio $1 : 1 : \sqrt{2}$ .

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