Chapter 8-4 part 2 Trigonometry This lesson has been modified from the original in the following ways: 1.Use of a trig. Table replaces a calculator. Students need access to a trig. table. a) rationale: CST questions are based on table and calculators are not allowed. Cheap accessible calculators can be used for trig. Students better understand the process involved with inverse trig. functions 2. Illustrations have been enlarged. 3. SohCahToa replaces original introduction. Teachers should tell the story of the old chief and his midnight encounter with a coffee table.

Lesson 4 Ex3 Use Trigonometric Ratios to Find a Length EXERCISING A fitness trainer sets the incline on a treadmill to 7°. The walking surface is 5 feet long. Approximately how many inches did the trainer raise the end of the treadmill from the floor? Let y be the height of the treadmill from the floor in inches. The length of the treadmill is 5 feet, or 60 inches. Answer: The treadmill is about 7.3 inches high. y =7.314 in =60 in

1.A 2.B 3.C 4.D Lesson 4 CYP3 A.1 in. B.11 in. C.16 in. D.15 in. CONSTRUCTION The bottom of a handicap ramp is 15 feet from the entrance of a building. If the angle of the ramp is about 4.8°, how high does the ramp rise off the ground to the nearest inch?

Lesson 4 Ex4 COORDINATE GEOMETRY Find m  X in right ΔXYZ for X(–2, 8), Y(–6, 4), and Z(–3, 1). Use Trigonometric Ratios to Find an Angle Measure

Lesson 4 Ex4 COORDINATE GEOMETRY Find m  X in right ΔXYZ for X(–2, 8), Y(–6, 4), and Z(–3, 1). Use Trigonometric Ratios to Find an Angle Measure from trig. table

A.A B.B C.C D.D Lesson 4 CYP4 A.66.0° B.56.3° C.33.7° D.24.0° COORDINATE GEOMETRY Find m  A in right ΔABC to the nearest degree.

Finding Missing Angle Measures Decide which Trig function to use based on the missing angle measure and the two given sides Substitute the given sides and the unknown variable into the function’s equation Calculate the value of the ratio Use the trig table to find the angle measure nearest the ratio value

Quick Examples (using Trig Tables) If Sin A =.3256, what is the m  A? = 19º If Tan A = 4.3, what is the m  A? ≈ 77º If Cos A =, what is the m  A? ≈ 39º If Sin A =, what is the m  A? ≈ 48.5º

Example #1 Solve for angle A A C B 15 in 5 in Hyp Opp SOH-CAH-TOA

Example #1 Solve for angle B A C B 15 in 5 in Hyp Adj SOH-CAH-TOA

Example #2 Solve for angle R R T S 10 7 Adj Opp SOH-CAH-TOA

Example #2 Solve for angle S R T S 10 7 Adj Opp SOH-CAH-TOA

Homework Chapter 8.4 pt 2 Pg ,11,18-23, , 45,49

Solving a Right Triangle To solve a right triangle you need to find all missing side lengths and angle measures. Sides are found using: –Pythagorean Theorem –Special Right Triangles or –Trig Ratios. Angles are found using: –Triangle Sum Theorem or –Inverse Trig Ratios.

Example #1 Solve for angle A A C B 15 in 5 in Hyp Opp 5  15=2 nd Sin -1 5  15 = 2 nd Sin -1 ( ) SOH-CAH-TOA

Example #1 Solve for angle B A C B 15 in 5 in Hyp Adj 5  15=2 nd Cos -1 5  15 = 2 nd Cos -1 ( ) SOH-CAH-TOA

Example #1 Solve for AC A C B 15 in 5 in

Example #2 Solve for RS R T S 10 7

X Z Y Adj Opp 7  10=2 nd Tan -1 7  10 = 2 nd Tan -1 ( ) SOH-CAH-TOA Example #3 Solve triangle XYZ

Homework Chapter 8-4 Pg 460 1,2,14-17,29- 37,44,46,47,48 Bring Calculators from now on!!!

Homework Chapter 8-4 Pg 460: # 1, 2, 10, 11, 14 – 17 all, 26, 29 – 49 odd