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From the top of a building, the angle of elevation of the top of a cell tower is 60° and the angle of depression to its foot is 45°. If distance of the building from the tower is 7 m, then find the height of the tower.

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Angle of elevation of the top of the tower = 60°. 

Angle of depression to the foot of the tower = 45°. 

Distance between tower and building = 7 m. 

Let the height of the building = x m and tower = y m. 

From the figure

tan 45° = \(\frac{x}{7}\)

1 = \(\frac{x}{7}\)

∴ x = 7 m. 

Also tan 60° = \(\frac{y-x}{7}\)

⇒ √3 = \(\frac{y-x}{7}\)

⇒ 7√3 = y – 7 

∴ y = 7 + 7√3 

= 7 (√3 + 1) 

= 7(1.732 + 1) 

= 2.732 × 7 

= 19.124 m.

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