how can we solve this?

Now consider the triangle ABC(diag. attached)

We have

angle B = 70 and angle A = 40

Therefore angle C = 70 (180-(40+70)).

Since angle b = angle c

therefore side AB= side AC = 10.

Now consider the triangle GFC

angle G = 90, and angle C in this triangle = 60 (130 -70 , in triangle ABC, angle C= 70)

and angle F = 30 (180 - (90+60)). NOw we have a 30-60-90 triangle.

Side CF = 8, therefore by 30-60-90 triangle properties ( sides distribute in the ratio = 1:\(\sqrt{3}\) :2)

We have GF = \(4\sqrt{3}\) and GC = 4.

Now to find AG, we know

AG = AC- GC

or AG = 10 -4 = 6.

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