Question

From the top of a tower a man finds that the angle depression of a csr on the ground is 30°. If the car is a distance 40 m from the tower. Find the height of the tower

Answer 1

Let AB be the tower and BC be the distance

Use tan 30 value to find the height as the angle of elevation is 30 degrees

Answer 2

Answer:

Height of the tower = $\frac{40}{\sqrt{3}} \mathrm{~m}$.

Explanation:

To find the height of the tower.

Step 1

Let A be the point the man exists standing. The angle his eye makes to the ground exists represented by the dotted line that exists $30^{\circ}$. This is the angle of depression So, the angle $A C B$ is also $30^{\circ}$. This is the angle of elevation. (Both the angles are exact because alternate interior angles are equivalent)

We need to find the height $\mathrm{AB}$.

Step 2

This can be estimated by using the trigonometric ratio

$\tan \theta=\frac{\text { opp.side }}{\text { adj.side }}$

Plugging in $\theta=30^{\circ}$, we get,

$&\tan =\frac{A B}{B C}$

$&\frac{1}{\sqrt{3}}=\frac{h}{40}$

$&h=\frac{40}{\sqrt{3}} \mathrm{~m}$

So, the height of the tower is $\frac{40}{\sqrt{3}} \mathrm{~m}$.

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