please please help me!!

Question

1. kayla tried parasailing. she was strapped into a parachute towed by a boat. An 800 ft line connected her parachute to the boat, which was at a 32 degree angle of depression below her. How high above the water is Kayla?

Answer 1

Answer 2

This is a fairly straightforward geometry problem involving a right triangle with a known angle and a known side. I would suggest you start with a diagram of a right triangle with the boat at a lower vertex, with Kayla at an upper vertex, and with the hypotenuse ( longest side) of the right triangle as the rope connecting Kayla to the boat.

The angle of depression is formed between the horizontal straight out from Kayla's position and her line of sight looking down to the boat. This will be one of the two acute angles in your right triangle. The measurement we are looking for will be the distance from the boat straight up towards the sky. This will be one of the legs of the right triangle, and it will be the leg that is across from the 32 degree angle.

If you have your diagram all set up, then what we will now do is set up an equation based on the definition of the sine ratio for right triangles. The sine ratio is "opposite side/hypotenuse" for any right triangle where the "opposite side" is the side across from the angle we're working with ( for this problem, it is the 32 degree angle). If we let "y" be the unknown side ( or the height ), the equation will be sin 32 = y/800. With a calculator, we find that sin 32 = 0.5299, so 0.5299 = y/800. Multiplying both sides by 800, we find that y is approximately 423.92, so Kayla is almost 424 feet above the surface of the water. I hope this makes sense!