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Right Triangle Trigonometry

Section 4-3. Right Triangle Trigonometry. 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.

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Right Triangle Trigonometry

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  1. Section 4-3 Right Triangle Trigonometry

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

  4. Trigonometric Functions θ adj opp sin  = cos  = tan  = csc  = sec  = cot  = hyp adj hyp hyp adj opp adj opp 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: hyp  the side opposite the acute angle , opp  the side adjacent to the acute angle , adj  and the hypotenuse of the right triangle. Memory Aide: SOH-CAH-TOA sine, cosine, tangent, cotangent, secant, and cosecant.

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

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

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

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

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

  10. Example 2: Application d = = 146.47. 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? observer horizontal 16○ angle of depression cliff42 m line of sight 16○ ship d The ship is 146.47 m from the base of the cliff.

  11. Example 3: Application sin  = = 0.875 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 angleof inclination. Does the painter’s plan satisfy the safetyrequirements for the use of the ladder? ladder house 16 14 θ Next use the inverse sine function to find .  = sin1(0.875) = 61.044975 The angle formed by the ladder and the ground is about 61. The painter’s plan is unsafe!

  12. Homework • WS 6-4

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