Word Problem Solving

Question

An 80-feet rope is attached to a boat 7 feet above the water level and a boy jumps over the wake while wakeboarding. What is the distance between his hands and the water level if the angle given is 87°?

Answer 1

If you draw a basic pic about this question, you will have a right angled-triangle. I draw the length from the rope(on the boat and I called that corner as A) to the boys hand (I called as C), and then an altitude from his hand to the water level (C). I need to find the length of CH. The question gives me an information about the distance between the boat and water level which is 7 feet. I drew an altitude from the point A to the water level and gave a name K.

When you complete this shape it's a trapezium, then I tried to make a right angled triangle, so I could use my triangle knowledge. I draw a straight line from the point C(which means from his hands) towards to the boat. I gave a name as B where the point hits to the altitute AK(the distance between the rope attached point at the boat and the water level). The angle is 90°. Now I have a right triangle is called ABC. When I mark 87° on BAC, I could see the angle ACB is 3°. I knew two angles and one side of the triangle ABC, so I could use SINE rule to find the lenght of AB. Because I knew AK is 7 feet. If I find AB, I subtruct from 7, so the answer will be the distance between his hand and the water level. Using my SINE rule a/sin87°=80/sin90°=x/sin3°. After using this equation I found x=4 (the length AB), so subtract from 7(the length AK). The answer is 3 (the length BK) BK is parallel to CH (You can see the rectangle ABCH), so BK=CH=3 feet.