Help me please please

  3.88 nm

Step-by-step explanation:

The angle at Port Latta between the actual direction of travel and the destination at Lookout Point is 90° -75° = 15°. The sine function relates the angle, the side opposite, and the hypotenuse of a right triangle, so you have ...

  sin(15°) = (distance to Lookout Point)/(15 nm)

Solving for the desired distance, we have ...

  distance to Lookout Point = (15 nm)sin(15°) = 3.88 nm

The yacht is 3.88 nautical miles from Lookout Point.

b) k’(6, 4); l’(3, 3)

step-by-step explanation:

a 270° clockwise rotation maps every point (x, y) to (y, -x). (it negates the x-coordinate and then switches it and the y-coordinate.)

this means the endpoints of the side congruent to kl, k' and l', would be mapped as:

k'(-4, 6)→(6, 4)

l'(-3, 3)→(3, 3)