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We will look at each of these trig functions from the right triangle perspective.

We will look at each of these trig functions from the right triangle perspective. Opposite Hypotenuse (opp) (hyp) Adjacent (adj). We will look at each of these trig functions from the right triangle perspective. Adjacent Hypotenuse

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We will look at each of these trig functions from the right triangle perspective.

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  1. We will look at each of these trig functions from the right triangle perspective. Opposite Hypotenuse (opp) (hyp) Adjacent (adj)

  2. We will look at each of these trig functions from the right triangle perspective. Adjacent Hypotenuse (adj) (hyp) Opposite (opp)

  3. SOH CAH TOA Right triangle formulas for Trig Functions: sin  = opp/hyp cos  = adj/hyp tan  = opp/adj

  4. a2 + b2 = c2 42 + 32 = c2 16 + 9 = c2 25 = c2 5 Example 1:Find the exact value of the six trig functions using the triangle given. 4 3

  5. sin  = opp/hyp = 3/5 cos  = adj/hyp = 4/5 tan  = opp/adj = 3/4

  6. a2 + b2 = c2 12 + b2 = 22 1 + b2 = 4 b2 = 3 3 Example 2:Find the exact value of the six trig functions using the triangle given. 2 1 

  7. sin  = opp/hyp = cos  = adj/hyp = 1/2 tan  = opp/adj =

  8. 20 m x Ex: 1 Figure out which ratio to use. Find x. Round to the nearest tenth. adj opp

  9. 283 m x Ex: 2 Find the missing side. Round to the nearest tenth. hyp opp

  10. Ex: 3 Find the missing side. Round to the nearest tenth. hyp 20 ft x adj

  11. Angles of Elevation & Depression

  12. Example 3: A tree casts a shadow that is 50 feet long. The angle of elevation to the top of the tree is 71.50. How tall is the tree?

  13. We know the adjacent side. We want to know the opposite side. Which trig function should we use? Example 3: A tree casts a shadow that is 50 feet long. The angle of elevation to the top of the tree is 71.50. How tall is the tree? 71.5 50 feet X

  14. Example 3: A tree casts a shadow that is 50 feet long. The angle of elevation to the top of the tree is 71.50. How tall is the tree? tan  = opp/adj tan 71.5 = x 50 2.99 = x 50 149.5 = x

  15. A safety regulation states that the maximum angle of elevation for a rescue ladder is 72. If a fire department’s longest ladder is 110 feet, what is the maximum safe rescue height? Ex. 2 110 feet x 72

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