I'll get you started with the first one . . .
As a cruise ship arrives in a new port of call, passengers are invited to admire
a particular famous statue at an angle of 20° from the direction of travel.
After the ship continues in the same direction for 575 m, the statue
appears to be at an angle of 68° from the direction of travel.
How far from the statue is the ship at the later time?
Of course, the first step is to make a sketch . . .
* * a
* 20° 112° * 68°
* - - - - - - - * - - - - D
A 575 B
The ship is at A and sights the statue at C: .
The ship sails to B: .
. . and sights the statue again: .
We want the distance:
Since , then
Law of Sines: .
We have: .
. . Therefore: .