Question

i want to know exact step by step answer for this​

Answer 1

Answer:

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Answer 2

ANSWER:-

Given:

A straight highways leads to the foot of a tower.A man standing at the top of the tower observes a car at an angle of depression of 30°, which is approaching the foot of the tower with uniform speed. 6 second later,the angle of depression of the car is found to be 60°.

To find:

Find the time taken by the car to reach the foot of the tower from this point.

Solution:

Let CD be the tower of height h m.& Let A be the initial position of the car and after 6 second, the car is found to be at B.

It is given that the angle of depression at A & B from the top of a tower be 30° & 60° respectively.

Let the speed of the car be v second per minute. So,

AB= Distance travelled by the car in 6s.

=) (6×v)sec. (distance=speed×time)

=) 6 seconds.

Let the car takes t minutes to reach the tower CD from B.

Then,

BC= distance travelled by car in t minute

=) (v×t)m

=) vt seconds.

Therefore,

In right ∆BCD,

$tan60 \degree = \frac{CD}{BC} \\ \\ = > \sqrt{3} = \frac{h}{vt} \\ \\ = > h = \sqrt{3} vt...........(1)$

In right ∆ACD,

$tan30 \degree = \frac{CD}{AC} \\ \\ = > \frac{1}{ \sqrt{3} } = \frac{h}{6v + vt} \\ \\ = > 6v + vt = \sqrt{3} h \\ \\ = > h = \frac{6v + vt}{ \sqrt{3} } ..............(2)$

Comparing equation (1) & (2), we get;

$\sqrt{3} vt = \frac{6v + vt}{ \sqrt{3} } \\ \\ = > \sqrt{3} \times \sqrt{3} vt = 6v + vt \\ \\ = > 3vt = 6 v + vt \\ \\ = > 3vt - vt = 6v \\ \\ = > vt(3 - 1) = 6v \\ \\ = > t \times 2 = 6 \\ \\ = > t = \frac{6}{2} \\ \\ = > t = 3 \: seconds.$

Hence,

The time taken by the car to reach the foot of the tower is 3 seconds.

Hope it helps ☺️