Radar tracking station o is 40 km away from a ship at point a. the ship travels east 45 km to point c at 30km/h. how long will the ship be on the radar with a 20 km radius?

From the given figure, segment OA = 40km, segment AC = 45km and segment OC = 20km
Angle OAC = 21 degrees.

Now, angle OBC = angle OCB because they are the angle formed at the intersection of the radius and the chord of a circle.

Using, sine rule, we find angle OCB.

Recall that sine rule states that


Thus,


Segment BC is a chord which makes angle 45.79 with the radius of the circle,
Using Pythagoras theorem, we have


Recall that time of a body travelling a distance, d, at v km/h is given by


Given that the ship travels at 30km/h, the time the ship will take on the radar covelling a distance of 27.89km is given by

the formula of a slope:

from a table we have

substitute:

the slope of f(x) is -1.

the graph of funcfion g(x) is a horizontal line. the slope of a horizontal line is equal 0. therefore the slope of g(x) is 0.

-1 < 0

answer: the function g(x) has the greatest slope.