Question

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

Answer 1

• See below

Explanation:

Angle opposite to 6 is complementary of α:

• 90 - α

Similarly, angle opposite to side 4 of the triangle in the right side is:

• 90 - β

Sum of the interior angles of the triangle on the bottom:

• 90 - α + 90 - β + γ = 180
• γ = α + β

• tan γ = tan (α + β)

From the smaller triangles we get:

• tan α = 4/6 = 2/3
• tan β = 3/4

Use the identity below and find the value of tan γ:

• 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