this is the finished product of my Depression Outline for my English Class.
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Geometry 8.4: 1
8.4 Angles of Elevation and Depression
Steve Keller Honors Geometry Thursday 2/8/2012 I.
Goals (Standards):
G-SRT.5. Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
G-SRT.7. Explain and use the relationship between the sine and cosine of complementary angles.
II.
Objectives:
Students will be able to find the angle of elevation given two side lengths using trigonometry.
Students will be able to find the angle of depression given two side lengths using trigonometry.
III.
Materials:
IV.
Chalkboard
Motivation: 1) Angles of Elevation (don’t give to them right away make them guess it) a.
I went to an IMAX theatre over Christmas break to see Mission Impossible: Ghost Protocol. I really enjoyed the movie, but afterword my neck neck was killing me. That got me thinking why. I was sitting in the front front row of a theatre, which is roughly 15 15 feet away from the screen. The bottom of the screen starts at eye level, but the center of the screen (where your eyes will be the most) is 26 feet up the screen. Know this why do you think my neck was hurting after the movie?
Probe for the students to come up with the answer. For a hint draw the diagram and ask what kind of trig ratio we are going to use. b. As you can see my neck was cranked at about about a 60 degree angle. Which is why my neck was hurting so bad. But what do we call this kind of problem.
Hint: it is in the title 8 .3. c.
THE KEY IS STARTING AT LINE OF SIGHT, OR EYE LEVEL.
2) Angles of Depression a.
I have another story for you. I went backpacking through Europe after my freshman year of college with with a friend of mine. We were on our way from Riensburg, Germany vising a friend to Verona, Italy to visit another friend. We took the train which goes through the Alps.
b. The guy managing the zip line to ld me that the zip line went 1 mile, all the way across this small town in the ravine of the Alps. He also told me the
Geometry 8.4: 2
drop was 11 degrees. So we went down and I quickly realized in terror that my feet were no longer near the ground as we dropped off a cliff. cliff. We ended up in a tree 5 feet feet above the ground. How far off the ground was I when I initially jumped off the cliff?
Draw the picture on the board board for them. Ask where the first line of our picture should go. (Line of sight, eye level)
Ask where our angle is going to be. (dropping 11 degrees down from line of sight)
Ask what is going to be 5280 feet (1 mile).
Ask how we are are going to figure figure out what initial initial height is. is. (sin (11) = x/5280. X=1007.5. Remember to add 5. Total height 1012.5 1012.5 feet)
What is this type of problem problem called? (angle of depression) 3) Examples a.
Imagine Vignesh is up in his room. Spots Bargav in the lawn at a 7 degree angle. Vignesh’s eye 15 feet off of the ground. How far away is Bargav?
Probe for where we are measuring up to from the ground (Vignesh’s eye so that we are eye level to star with)
Tan(7)=15/x. x=122.2 feet away
What type of problem is this? (angle of depression b. (Hated in high school) 12 foot wall. 15 foot ladder. What is the angle angle from the floor to ladder if the top of the ladder just touches the top o f the wall.
Tan(x)=12/15. X=38.7 degrees c.
Red Hen sign. I have to look up at the top of the sign at an angle of 75 degrees 40 feet from the sign.
Tan (75) = x/40. X=149.3 feet
EYE LEVEL
but I am 6.25 feet t all so, the final answer: 155.5
What type of problem is this? (angle of e levation)
Ask the students what trig function function we seem to be using the most. Why? (tan, because we usually know/want to to know the lateral or vertical distances or the angle. We rarely are looking for the hypotenuse.)
