Krishna
0

Step 1: Analyse the give data and construct an imaginary figure by the given hints.

GIVEN: The angles of elevation of the top of the tower from the two points

are complementary angles.

Let, if you say angle of elevation \angle ADC = \theta

then, angle of elevation \angle ACB = 90\degree - \theta

The distance between the pole and points

BC = 4 cm

DB = 9m

Height of the tower AB = ?

Step 2: Determine the height of the tower by using the trigonometric ratios

From the figure:

\tan \theta = \frac{opposite}{adjacent} = \frac{AB}{DB}

\tan \theta = \frac{AB}{9}.....................(1)

Take right triangle ACD

\tan (90\degree - \theta) = \frac{AB}{CB}

\cot \theta = \frac{AB}{4}.................(2)        (\because \tan (90\degree - \theta) = \cot \theta )

Step 3: Multiplying equation (1) and (2)

\tan \theta = \frac{AB}{9}..................(1)

\cot \theta = \frac{AB}{4}.................(2)

Multiply

\cot \theta * \tan \theta = \frac{AB}{4} * \frac{AB}{9}

\frac{1}{\tan \theta} *\tan \theta = \frac{AB^2}{36}     (\because \cot \theta = \frac{1}{\tan \theta} )

1 = \frac{AB^2}{36}

AB^2 = 36

AB = \sqrt{6*6}

AB = 6 m

The height of the tower = 6 m