Calculate 64514

In the triangle ABC, a: b = 3: 2 and α: β = 2: 1. Calculate the ratio a: c.

Correct answer:

r =  6:5

Step-by-step explanation:

r1=a:b=3:2 α:β=2:1 α=2β sinα:sinβ=a:b=3:2  sin2β:sinβ=3:2=1.5 sinβ2 sinβcosβ=1.5 2 cosβ=1.5 cosβ=0.75  β=π180°arccos0.7541.4096  α=2 β=2 41.409682.8192  γ=180αβ=18082.819241.409655.7711   r=sinγsinα=a:c r=sinα/sinγ=sin82.819244218542° /sin55.771133672187° =0.992157/0.826797=1.2=56=151=1.2=6:5

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