Given: △fkl, fk=a

m∠f=45°, m∠l=30°

find: fl
i know that i need to add an altitude from k so i can get a 45, 45, 90 triangle and a 30, 60, 90 triangle, but after that, i keep getting the answer wrong.

Step-by-step explanation:

As given  in figure 1 below:

FK = a, m∠F = 45° and m∠L = 30°

Construction: Draw an altitude KE from point K on FL.

Now, In ΔFEK,

FE = EK (Sides opposite to equal angles of a triangle)

Let FE = EK = x  

Now, using pythagoras In  ΔFEK,

∴ FE = EK =

Now in ΔEKL, EK =

Using trigonometry ratio,

TanФ = Altitude\ Base

Tan 30° =

Now FL = FE + EL

FE = and

∴

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