SOLUTION: in tringle ABC,right angle is at b,bc=x, and ab=2x then determine angle a and angle c.

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Question 898135: in tringle ABC,right angle is at b,bc=x, and ab=2x then determine angle a and angle c.
Found 2 solutions by Fombitz, MathTherapy:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
AB=2x
BC=x
Using the Pythagorean theorem,
AB%5E2%2BBC%5E2=AC%5E2
%282x%29%5E2%2Bx%5E2=AC%5E2
AC%5E2=5x%5E2
AC=sqrt%285%29x
Then,
sin%28C%29=%282x%29%2F%28sqrt%285%29x%29=2%2Fsqrt%285%29=%282%2F5%29sqrt%285%29
A=63.4
sin%28A%29=%28x%29%2F%28sqrt%285%29x%29=sqrt%285%29%2F5
B=26.6

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
in tringle ABC,right angle is at b,bc=x, and ab=2x then determine angle a and angle c.




BC = x, and AB = 2x

Therefore, tan ∠A = O%2FA, or BC%2FAB, or x%2F2x, or 1%2F2

∠A = tan%5E-1%281%2F2%29

∠A = highlight_green%2826.565%5Eo%29

∠C = 90%5Eo+-+26.565%5Eo = highlight_green%2863.435%5Eo%29