NCERT Example 5 — Some Applications of Trigonometry

NCERT Example

Example 5

shadows · altitude of sun

The shadow of a tower is 40 m longer when the Sun's altitude is 30° than when it is 60°. Find the height of the tower.

Board-exam working:

Let AB = h m and BC = x m. Then BD = x + 40 m.

Using triangle ABC:

\tan60^\circ=\frac{AB}{BC}

\sqrt3=\frac{h}{x}

h=x\sqrt3\qquad\text{(1)}

Using triangle ABD:

\tan30^\circ=\frac{AB}{BD}

\frac1{\sqrt3}=\frac{h}{x+40}

h=\frac{x+40}{\sqrt3}\qquad\text{(2)}

Equating (1) and (2):

x\sqrt3=\frac{x+40}{\sqrt3}

3x=x+40

x=20

h=20\sqrt3\text{ m}

The height of the tower is 20√3 m.