Question

An observer from the top of a light house, 100 m high above sea level, observes
the angle of depression of a ship, sailing directly towards him, changes from
30° to 60°. Determine the distance travelled by the ship during the period of
observation​

Answer 1

Answer: 115.46 m

Step-by-step explanation:

Answer 2

Step-by-step explanation:

let AB be the tower of height 100m and let D and C be the initial and final positions of the boat. let y be the distance travelled by the ship during the period of observation and x be the distance between the tower and the ship.

in ΔABC, tan 60 = 100/x

=> √3= 100/x

=>x = 100/√3 m

inΔABD, tan 30 = 100/(x +y)

=>1/√3= 100/(x + y)

=> x+y = 100√3

=> 100/√3 + y = 100√3

=>y = 100√3 - 100/√3

=> y = (200√3)/ 3

=> y = (1.732 *200)/ 3

=>y = 115.46m

so the distance travelled by ship during period of observation = 115.46m