Hello, katelynn!

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 . . . Code:

C
*
* *
*48°*
* *
* * 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

In

Law of Sines: .

We have: .

. . Therefore: .