Angles of Elevation and Depression Do you remember your… SOHCAHTOA?

Angles of Elevation and Depression Bird’s line of sight Angle of Depression Angle of Elevation Cat’s line of sight The lines of sight are parallel to each other, making the angles of elevation and depression alternate interior angles which are… CONGRUENT!!! So whether you are looking for an angle of elevation or an angle of depression, FIND THE HORIZONTAL and the angle formed off of it. They will be congruent!

So for some problems: The angle of elevation to a building in the distance is 22 degrees. You know that the building is approximately 450 ft tall. Estimate the distance to the base of the building. 2. Set up an equation 1. Draw a diagram 450 ft 22 3. Solve! x X = 1113.8 ft away!

From on the second level of the Eiffel Tower, Pierre sees two friends, one to the left, one to the right. If he is 125m high and his friend to the right is at an angle of depression of 23.5 degrees and his friend to the left is at an angle of depression of 64.3 degrees, how far apart are his friends? 125m 23.5 64.3 Remember, it doesn’t matter whether it is an angle of elevation or depression, you MUST start from a horizontal! Friend on the left Friend on the right

To solve your triangle… 125m 64.3 Friend on the left 23.5 Friend on the right x y You will have to solve two separate problems to find x and y. The total distance between the friends is x + y. X = 60.2 m Y = 287.5 m Total distance is x + y = 347.6 m (Never round till the end)

Amy is in a kayak 200 ft from the Statue of Liberty Amy is in a kayak 200 ft from the Statue of Liberty. She sees the book in the statue’s arm at an angle of elevation of 36.7 degrees and the top of the flame at an angle of 48.7 degrees. From her point of view, one is directly above the other. About how much higher the flame is than the book. You will have to solve each triangle separately to find the distance in the height. 48.7 36.7 200 ft

X – Y = about 79 ft Flame Find the height of the flame x Book X = 227.7 ft Find the height of the book y 48.7 36.7 Y = 149.1 ft 200 ft Find the distance between the book and the flame, SUBTRACT! X – Y = about 79 ft

Are you still a little confused? Check out these websites if you need some more practice on your own: http://www.algebralab.org/Word/Word.aspx?file=Trigonometry_AnglesElevDepression.xml http://www.tutorvista.com/content/math/trigonometry/heights-and-distances/angles-elevation-depression.php http://www.mathwarehouse.com/geometry/angle/elevation_depression/

Special Right Triangles 30°- 60°- 90° 45°- 45°- 90°

45°- 45°- 90° Triangles The lengths of the sides of a 45°- 45°- 90° triangle are in the ratio of

Example 1: Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are both 3 inches Solution: Step 1: This is a right triangle with two equal sides so it must be a 45°- 45°- 90° triangle. Step 2: You are given that the both the sides are 3. If the first and second value of the ratio              is 3 then the length of the third side is     

Example 2: Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is      inches and one of the angles is 45° Solution: Step 1: This is a right triangle with a 45°so it must be a 45°- 45°- 90° triangle. Step 2: You are given that the hypotenuse is      . If the third value of the ratio             is      then the lengths of the other two sides must 4.

30°- 60°- 90° Triangles The lengths of the sides of a 30°- 60°- 90° triangle are in the ratio of

Test the ratio of the lengths to see if it fits the ratio. Example 1: Find the length of the hypotenuse of a right triangle if the lengths of the other two sides are 4 inches and       inches. Solution: Step 1: Test the ratio of the lengths to see if it fits the              ratio. Step 2:  Yes, it is a 30°- 60°- 90° triangle for n = 4 Step 3:  Calculate the third side. 2n = 2×4 = 8 Answer: The length of the hypotenuse is 8 inches.

This is a right triangle with a 30° angle so it must be a Example 2: Find the lengths of the other two sides of a right triangle if the length of the hypotenuse is 8 inches and one of the angles is 30°. Solution: Step 1: This is a right triangle with a 30° angle so it must be a 30°- 60°- 90° triangle. Step 2: You are given that the hypotenuse is 8. Substituting 8 into the third value of the ratio             , we get that 2n = 8 so n = 4. Substituting n = 4 into the first and second value of the ratio we get that the other two sides are 4 and      .

Still confused? Check these out: 30-60-90 triangle only: http://www.mathopenref.com/triangle306090.html 45-45-90 triangle only: http://www.mathopenref.com/triangle454590.html Great practice with all special triangles and trig: http://regentsprep.org/Regents/Math/math-topic.cfm?TopicCode=rtritrig

Ok, now you have to show me you know your stuff! Print out the worksheet on Angles of Elevation and Depression and Special Right Triangles. SHOW ALL YOUR WORK!!!