Chad and Lis were going hiking together on a sunny day. They're both in the same geometry class together. Their teacher, Mr. Homeworkallthetime has asked them to find real world applications of trigonometry and they decided outside would have a lot of options.
What are we going to do? I can't swim!
If the angle of the tree to the ground is 26 degrees, and the distance from the treetop to the other side looks to be around 30ft, then we can do 30cos26=x. If x represents the width of the river, then the river is around 27ft across.
We can use the trig skills Mr. Homeworkallthetime taught us to build a raft!
Hey, you see those hills over there? Do you think we could use trig to find the angle of the valley?
Probably, but you get to solve it this time.
So, if the valley is theta, the length from the angle to the tip of the left hill is about 15m which is H. The height of the left hill is about 12m representing A. To solve this, you would do cos^-1(12/15) which equals 36.869 degrees.
WE ARE NERDS
Let's say the bottom right angle is 50 degrees , and the opposite side is 10 feet. Using 10tan50, we can conclude the width of the cave is 11.918 feet.