Question

the angle of depression of a car standing on the ground from the top of a 66 m tower is 30° .find the distance of a car from the base of the tower

Answer 1

Answer:

The distance of a car from the base of the tower is 114.312 m.

Step-by-step explanation:

In the figure below,

AB denotes the tower of length 66 m and C denotes the position of car. thus, CB be the distance of the car and base of tower. and ∠C denotes the angle between car and top of tower  so,  ∠C=30°.

We have to find the length CB.

In Δ ABC ,

$\tan C=\dfrac{\text{perpendicular}}{\text{base}}$

$\tan 30^{\circ}=\frac{AB}{CB}$

$\tan 30^{\circ}=\frac{66}{CB}$

Also , by trigonometric table, $\tan 30^{\circ}=\frac{1}{\sqrt{3}}$

$\frac{1}{\sqrt{3}}=\frac{66}{CB}$

${CB}=66 \times {\sqrt{3}}$

Also, value of ${\sqrt{3}}=1.732$

then, ${CB}=66 \times 1.732$

${CB}=114.312$

Thus, the distance of a car from the base of the tower is 114.312 m.

Answer 2

Answer:

Tan30 =p/b

so 1/root3=66/base

therefore base=66root3