Question

a highway leads to a foot of 300m high tower. an obeservatory is set at the top of the tower . it sees a car moving towards it at an angle of depression 30 degrees . after 15seconds angle of depression becomes 60degrees. find the distance travelled by the car.

Answer 1

Answer:

Step-by-step explanation:

1 pic was 3 part

2 pic was 2 part

3 pic was 1 part

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Answer 2

Given: A highway leads to a foot of 300m high tower. an obeservatory is set at the top of the tower . it sees a car moving towards it at an angle of depression 30 degrees . after 15seconds angle of depression becomes 60degrees.

To find: The distance travelled by the car.

Solution:

In order to solve the given question, refer to the attached figure. CD is the distance travelled by the car in 15 seconds. As evident from the figure, the angle of 30° can be written as follows.

$tan 30 = \frac{AB}{BC}$

$\frac{1}{\sqrt{3} } = \frac{300}{BC}$

$BC = 300\sqrt{3} units$

Similarly, the angle 60° can be written as shown below.

$tan 60 = \frac{AB}{BC+CD}$

$\sqrt{3} = \frac{300}{300\sqrt{3}+CD }$

$CD\sqrt{3} =600$

$CD = 346.41$

The length of CD is 346.41 m and hence, the distance that was covered by the car while moving towards the tower is 346.41 m.

Therefore, the distance travelled by the car is 346.41 m.