1. Right Triangle Trigonometry Section 4-3

2. 2 Objectives I can use Special Triangle Rules I can identify how the 6 trig functions relate to the memory aide SOH-CAH- TOA I can use SOH-CAH-TOA to find information from right triangles and word problems

3. Special Right Triangles 30 o, 45 o, 60 o 60 o Use the pythagorean theorem to find the sides. You must memorize these!!! The x-value is the cosine of that angle. The y-value is the sine of that angle.

4. 4 The six trigonometric functions of a right triangle, with an acute angle , are defined by ratios of two sides of the triangle. The sides of the right triangle are:  the side opposite the acute angle ,  the side adjacent to the acute angle ,  and the hypotenuse of the right triangle. Memory Aide: SOH-CAH-TOA sine, cosine, tangent, cotangent, secant, and cosecant. opp adj hyp θ Trigonometric Functions sin  = cos  = tan  = csc  = sec  = cot  = opp hyp adj hyp adj opp adj

5. 5 Calculate the trigonometric functions for . The six trig ratios are 4 3 5  sin  = tan  = sec  = cos  = cot  = csc  = Example: Six Trig Ratios

6. 6 Calculator Mode MUST be set to DEGREES!!

7. 7 Finding an Angle 2 5  Example: Six Trig Ratios We have the opposite side and hypotenuse Sin θ = 2/5  = sin -1 (2/5) = 23.6°

8. 8 Word Problems Always draw a picture or diagram to represent the situation.

9. 9 angle of elevation When an observer is looking downward, the angle formed by a horizontal line and the line of sight is called the: Angle of Elevation and Angle of Depression When an observer is looking upward, angle of elevation. the angle formed by a horizontal line and the line of sight is called the: observer object line of sight horizontal observer object line of sight horizontal angle of depression angle of depression. Angle of Elevation and Angle of Depression

10. 10 Example 2: A ship at sea is sighted by an observer at the edge of a cliff 42 m high. The angle of depression to the ship is 16 . What is the distance from the ship to the base of the cliff? The ship is 146.47 m from the base of the cliff. line of sight angle of depression horizontal observer ship cliff 42 m 16 ○ d Example 2: Application d = = 146.47.

11. 11 Example 3: A house painter plans to use a 16 foot ladder to reach a spot 14 feet up on the side of a house. A warning sticker on the ladder says it cannot be used safely at more than a 60  angle of inclination. Does the painter’s plan satisfy the safety requirements for the use of the ladder? Next use the inverse sine function to find .  = sin  1 (0.875) = 61.044975 The painter’s plan is unsafe! ladder house 16 14 The angle formed by the ladder and the ground is about 61 . θ Example 3: Application sin  = = 0.875

12. 12 Homework WS 6-4