Question

A man on the top of a vertical tower observes a car moving at a uniform speed. If it takes 8 minutes for the angle of depression to change from 30° to 60°, Find the time taken by car reach the tower?

solve by process ​

Answer 1

Step-by-step explanation:

see the attachment for answers

$\huge\color{purple}{ \colorbox{orange}{\colorbox{white} {Thanks}}}$

Answer 2

Here, ZACB = 30° and ZADB = 45.

Let C denote the initial position of the car and D be its position after 12 minutes. Let the speed of the car be x metre/minute, then

CD=12x metres

Speed Time)

(" Distance =

Let the car take t minutes to reach the tower from D. Then,

DB = tx metres

Now in the right-angled triangles ACB,

tan 30¹ = AB/CB

→ 1/√3=AB/(CD + DB)

1/√3 = AB/(12x+1x)

AB=(12x+tx)/√3 (1)

Also, in the right-angled triangle ADB,

tan 45¹ = AB/DB

1= AB/DB

→ AB = DB = tx

(2)

From (1) and (2), we have

t=12/(√3-1)=12(√3+1/2

= 6(√3+1)

= 16.39

Time = 16.39 minutes

= 16 minutes 23 seconds