#### The angle of elevation of the top of a building from the foot of the tower is 30 \degree and the angle of elevation of the top of the tower from the foot of the building is 60º. If the tower is 30 m high, find the height of the building.

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Krishna

0

Step 1: Examine the given problem and draw a imaginary figure

Height of the tower PQ = 30 m

The angle of elevation of the top of the building from the foot of the tower = 30\degree

The angle of elevation of the top of the tower from the foot of the building = 60 \degree

Height of the building AB = h say

Step 2: Find the distance between the building and tower

NOTE: We know opposite side of the right angle triangle and we have to calculate the adjacent side.

So, use \tan \theta = \frac{opposite}{adjacent}

From the figure: Right triangle PQB

\tan 60\degree = \frac{PQ}{BQ}

\tan 60\degree = \frac{30}{BQ}

\sqrt{3} = \frac{30}{BQ} \because \tan 60\degree = \sqrt{3}

BQ = \frac{30}{\sqrt{3}}......................(1)

Step 3: Find the height of the building

From the figure: right triangle ABQ

\tan 30\degree = \frac{AB}{BQ}

\frac{1}{\sqrt{3}} = \frac{h}{BQ} \because \tan 60\degree = \frac{1}{\sqrt{3}}

h \sqrt{3} = BQ

h \sqrt{3} = \frac{30}{\sqrt{3}} \because Equation (1)

h = \frac{30}{\sqrt{3} * \sqrt{3}}

h = \frac{30}{3}

h = 10 m

The height of the building = 10 m