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coldgirl [10]
2 years ago
9

Find an equation for y (in terms of β and α). Then find tan y.

Mathematics
2 answers:
dmitriy555 [2]2 years ago
7 0

This can be expanded through the tangent angle addition formula:

tan(α+β)=tanα+tanβ1−tan -α + tanβ

Thus,tan(x+y)=tanx+tany1−tan x tany

Hope it helps you

avanturin [10]2 years ago
5 0

Answer:

  • See below

Step-by-step explanation:

<u>Angle opposite to 6 is complementary of α:</u>

  • 90 - α

<u>Similarly, angle opposite to side 4 of the triangle in the right side is:</u>

  • 90 - β

<u>Sum of the interior angles of the triangle on the bottom:</u>

  • 90 - α + 90 - β + γ = 180
  • γ = α + β
  • tan γ = tan (α + β)

<u>From the smaller triangles we get:</u>

  • tan α = 4/6 = 2/3
  • tan β = 3/4

<u>Use the identity below and find the value of tan γ:</u>

  • tan (α + β) = (tan α + tan β)/(1 - tan α tan β)
  • tan γ =
  • tan (α + β) =
  • (2/3 + 3/4) / (1 - 2/3*3/4) =
  • (17/12) / (1/2) =
  • 17/6 =
  • 2 5/6
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