Olly the Octopus pokes his head up from the waves to see what is going on on the shore. To his dismay, he sees a fisher. The fisher seems to be standing directly straight ahead of where his best fish friend is. Olly is 5 yards from his friend. If he is looking at the fisher at a 56 degree angle, Olly wonders how far the fisher is from his fishy friend.
Luckily, Olly knows trigonometry. He does tan(56)=x/5 or 5*tan(56)=x. and he figures out that the fisher is about 1.5 yards from his friend.
Using trigonometry, Olly does the sin(58)=8/x or 8/sin(58)=x. He figures out that he must swim about 9.5 yards to his friend.
Olly quickly goes down below the surface to warn his friend. When he is 8 yards from the ground, he sees his fish friend. He estimates that he is looking at the fish at a 58 degree angle. He wants to know how far he has to swim to get to his friend to warn him about the fisher.
His fish friend is frightened about the fisher. Olly comforts him and says they can find somewhere to hide, so they won't be tempted by the worm. The fish spots a cave in the distance and says we can hide there.
If the plant is 4 yards from the cave, the horizontal line where they started is 8 yards from the cave. He knows the sin of the angle should equal 8/11. He does sin^-1 (8/11) equals the angle. The angle they are swimming at is approximately 46.66 degrees.
They swim together towards the cave. As they are swimming, Olly wonders what the angle are they swimming at compared to the horizontal line where they started. He knows that when they started they had to swim 11 yards to the cave. He also knows that they are even with the plant and the plant is 4 yards from the cave. The plant is also halfway from the cave to the horizontal line where they began. Does he have enough information to find out the angle?
This whole line is 11
They make it safely to the cave. Olly shares his knowledge of math and trigonometry with his friend, until the fisher is long gone. They then go out and finish a beautiful day in the ocean.