Hector and His Island

This is Hector. He has been trapped on this island for 5 years. The island has lots of varying foods. Also, this island has many animals including Hector's pet dog Chonky.

Hector wants to know how tall his door is from the ground. If the tree is 10 ft away, and the angle of elevation is 68°. Then he knows that the Tangent of 68° then he multiplies that by 10 and gets his height which is 8.08 ft tall. He now wants to explore the island.

20 ft

X

68°

Hector jumped over to this part of the island but he doesn't know if his dog Chonky can. He needs to know how far away Chonky is from him.

If he knows that his hypotenuse is 5.8 ft long and the angle of depression is 58° and that means he needs to use cosine to find his length between him and Spot. X/5.8 ft so that means Cos(58°) * 5.8 = 3.07 ft away. And after he helped Chonky over he's now pretty thirsty.

X

58°

5.8 ft

58°

68°

Hector wants to get a coconut off of the palm tree. If he knows that his hypoteneuse is 8 ft and his opposite side is 7ft then he needs to find his angle of elevation. He needs to use Sin to find his angle of depression. If the Sin^-1(7/8) then his angle of depression is 61.04°

X

8FT

7FT

X

Now that Hector has a house, has explored his island more, and has water and coconuts, he wants to hang out under a tree and relax with Chonky dog.

Sadly though, Hector has to escape the island with Chonky dog because he accidentally started a forest fire when boiling some water.

The End

To be continued...