9.3 Finding Missing Sides and Angles Secondary Math II 9.3 Finding Missing Sides and Angles

Warm-UP Write the three trigonometric functions. Find the three trig values for 𝛼 in the triangle.

Math tutoring is available in the LIBRARY Monday-Friday 3:00-4:00. (Mrs. Sakurada is there on Tuesdays) Attendance recovery is offered—you can go there and work on homework and recover attendance credit for any class! (5 hours=.25 credit)

What you will learn I will be able to use the trigonometric ratios to solve for missing sides and angles on a right triangle.

Using Trig to find Missing LENGTHS Given: 1 side length, and 1 angle measurement (not the 90° angle)   17 x

Three different cases can happen:   h o sine   a o tangent   h a cosine

Solving for Missing LENGTHS Look at the angle you are given What is the known side in relation to that angle? What is the unknown side in relation to that angle? Set up the trig ratio with those two lengths Sine Cosine Tangent Solve for the missing length.

Sine Examples   x 12 15 x  

Find “sin” “cos” and “tan” on your calculator or trig table Whenever you see sin 𝜃 , cos 𝜃 , tan 𝜃 , you need to realize they are just numbers (the numbers on the trig table), or stored in a calculator

Calculator People Check your MODE!!!!! Type in sin 42 Type in cos⁡27 Press Mode Look for Degree or Radian Degree should be highlighted (we will use radians next year in Math 3) Type in sin 42 Type in cos⁡27 Type in tan 14

Cosine Examples   13 x x   10

Tangent Examples   x 7 9 x  

Word Problem Example: You are looking up at a hippo standing on the top of the Roy High marquee sign. The angle of elevation is 42°. You are 20 feet away from the marquee sign. How far off the ground is the hippo?

9.3 Worksheet Problems

Word Problem Example: Buckbeak, the hippogriff, is being held captive in a tower. Harry Potter is on the ground below with a ladder. When Harry stands 15 feet from the base of the tower and looks up at the hippogriff, the angle of elevation to the hippogriff is 60 degrees. How long does the ladder have to be for Harry to rescue Buckbeak?

Using Trig to find Missing ANGLES Look at the missing angle. What are the sides you have in relation to that angle (opp, adj, hyp) Set up the trig ratio with those two lengths Sine Cosine Tangent Solve for the missing angle Trig Table or Calculator

Solve for Missing Angle Trig Table Calculator Which sides are you using, which trig ratio is appropriate? Write it out 𝑐𝑜𝑠𝜃= 6 11 6 11 =0.5454… Find the decimal under cosine The angle is 57°. We ‘undo’ functions with their inverse: 2nd, then the trig button 𝑠𝑖𝑛 −1 𝑐𝑜𝑠 −1 𝑡𝑎𝑛 −1 𝜃= cos −1 6 11

9.3 Worksheet Problems

9.3 Worksheet Problems