A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/6$ . If side C has a length of $5$ and the angle between sides B and C is $( pi)/2$ , what are the lengths of sides A and B?

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Answer 1 · 2018-07-24T13:15:19

$A=10$ & $B=5\sqrt3$

The angle between sides $A$ & $C$

$=\pi-\frac{\pi}{6}-\pi/2$

$=\pi/3$

Now, using Sine rule in the given triangle as follows

$\frac{A}{\sin(\pi/2)}=\frac{B}{\sin(\pi/3)}=\frac{C}{\sin(\pi/6)}$

$\frac{A}{1}=\frac{B}{\sqrt3/2}=\frac{5}{1/2}$

$A=2/\sqrt3 B=10$

$\implies A=10$ &

$B=\sqrt3/2\times 10$

$=5\sqrt3$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/6(pi)/6. If side C has a length of 5 5 and the angle between sides B and C is ( pi)/2( pi)/2, what are the lengths of sides A and B?