Breakout Session #2 Right Triangle Trigonometry 4/25/2018 1:57 AM Breakout Session #2 Right Triangle Trigonometry Presented by Dr. Del Ferster © 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries. The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

A quick look at today’s activities We’ll spend some time on an “INTRO” to trig. I have a video to show you, in case you are inclined to teach trig to your students. We’ll work on the TRIG RIVER ACTIVITY We’ll work on some “test-like” questions I know that we usually do these first, but I believe that we’ll benefit more by spending some time looking at the basics of trigonometry together. 

3 Basic Trigonometric Functions SINE COSINE TANGENT

Represents an unknown angle Greek Letter q Prounounced “theta” Represents an unknown angle

Labeling Right Triangles The most important skill you need right now is the ability to correctly label the sides of a right triangle. The names of the sides are: the hypotenuse the opposite side the adjacent side

Labeling Right Triangles The hypotenuse is easy to locate because it is always found across from the right angle. Since this side is across from the right angle, this must be the hypotenuse. Here is the right angle...

Labeling Right Triangles Before you label the other two sides you must have a reference angle selected. Lots of books label this as It can be either of the two acute angles. In the triangle below, let’s pick angle B as the reference angle. A B C This will be our reference angle...

Labeling Right Triangles Remember, angle B is our reference angle. The hypotenuse is side BC because it is across from the right angle. A B (ref. angle) C hypotenuse

Labeling Right Triangles Side AC is across from our reference angle B. So it is labeled: opposite. A B (ref. angle) C hypotenuse opposite

Labeling Right Triangles Adjacent means beside or next to The only side unnamed is side AB. This must be the adjacent side. A B (ref. angle) C adjacent hypotenuse opposite

Labeling Right Triangles Let’s put it all together. Given that angle B is the reference angle, here is how you must label the triangle: A B (ref. angle) C hypotenuse adjacent opposite

Labeling Right Triangles Given the same triangle, how would the sides be labeled if angle C were the reference angle? Will there be any difference?

Labeling Right Triangles Let’s put it all together. Given that angle C is the reference angle, here is how you must label the triangle: A B C (ref. angle) hypotenuse opposite adjacent

Labeling Practice Given that angle X is the reference angle, label all three sides of triangle WXY. Do this on your own. Click to see the answers when you are ready. W X Y

Labeling Practice How did you do? W X Y adjacent opposite hypotenuse

SOH CAH TOA

Sample keystroke sequences Sample calculator display Rounded Using a Calculator You can use a calculator to approximate the sine, the cosine, and the tangent of 74º. Make sure your calculator is in degree mode. The table shows some sample keystroke sequences accepted by most calculators. Sample keystroke sequences Sample calculator display Rounded approximation 74 or sin Enter 0.961261695 0.9613 74 or cos Enter 0.275637355 0.2756 74 or tan Enter 3.487414444 3.4874

Finding a Side Using trig functions to find the length of a missing side.

tan 71.5° y tan 71.5° y = 50 (tan 71.5°) y = 50 (2.98868) A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? tan 71.5° y tan 71.5° 71.5° y = 50 (tan 71.5°) 50 y = 50 (2.98868)

200 60° x cos 60° x (cos 60°) = 200 x X = 400 yards A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? cos 60° x (cos 60°) = 200 200 60° x x X = 400 yards

Finding an Angle Using trig functions to find the measure of one of the acute angles.

Redraw the figure and mark on it HYP, OPP, ADJ relative to the unknown angle Steps to finding the missing angle of a right triangle using trigonometric ratios: OPP  5.92 km 2.67 km ADJ HYP

For the unknown angle choose the correct trig ratio which can be used to set up an equation Set up the equation Steps to finding the missing angle of a right triangle using trigonometric ratios: OPP  5.92 km HYP 2.67 km   ADJ  

Steps to finding the missing angle of a right triangle using trigonometric ratios: Solve the equation to find the unknown using the inverse of trigonometric ratio. OPP  5.92 km   HYP 2.67 km   ADJ  

Practice Together: Find, to one decimal place, the unknown angle in the triangle.  3.1 km 2.1 km

YOU DO: Find, to 1 decimal place, the unknown angle in the given triangle.  7 m 4 m