WPP 12: Unit O Concept 10: Solving angle of elevation and depression word problems

Introduction: Hannah's Hike

 
(http://www.destination360.com/north-america/us/vermont/vermont-hiking)

The Problem: Hannah's Hike

After all the bow business and shopping, Hannah takes time to appreciate nature by going on a hiking trip with her friends. She is determined to hike up the cliff and be able to look down the side of the cliff to see the ledge where most people jumped off after such a long hike! (Don't worry it's safe even though it's 300 feet!)

1) Before they start their hike, Hannah wants to know the height of the cliff. The pole where she is standing from is 600 feet away from the cliff itself. She knows from the base of the pole to the base of the flagpole, there is an angle of elevation of 45 degrees. What is the total height of the cliff? (Round to the nearest foot!)

2) After reaching the top of the cliff, Hannah lies down next to the flag pole and looks down towards the tip of the ledge. She estimates the angle of depression from where she is lying to the tip of the ledge to be 21 degrees. If the ledge is 300 feet higher from the ocean floor, what is the distance she is looking at from the base of the flagpole to the tip of the ledge? (Round to the nearest foot!)

The Solution: Hannah's Hike

(This is a visual of what Hannah's hike looks like)

First we need to find the height of the cliff (we'll need this piece of evidence for problem #2). We know we must use trig functions to be able to find the missing side we're looking for. Remember that in an angle of elevation, there will be a horizontal line then the angle will go upwards.

Next, we can use the height we found earlier and other clues to find the side labeled "opp." to help us solve the whole problem. Again, we use trig functions to find the desired side. Remember that in an angle of depression, there is a horizontal line but the angle will go downwards.