Extended Sine Rule Practice Problems Online

In triangle $ABC$ , let $a, b$ and $c$ be the lengths of the legs of a triangle opposite vertices $A, B, C$ respectively. Let $\alpha, \beta, \gamma$ be the values of the respective angles. What is the value of

$a ( \sin \beta - \sin \gamma) + b ( \sin \gamma - \sin \alpha ) + c ( \sin \alpha - \sin \beta )?$

Triangle $ABC$ is inscribed in a circle $\Gamma$ . If $\angle A = 60^{\circ}$ and the length of the side opposite to vertex $A$ is $49 \sqrt{3}$ , what is the radius of $\Gamma$ ?

In triangle $ABC$ , $\angle ABC = \frac{ \pi}{2}$ . If $AC = 12$ , what is the radius of the circumcicle of $ABC$ ?

Triangle $ABC$ has $\angle A=150^{\circ}$ and $\overline{BC}=7$ . If the area of the circumscribed circle of $ABC$ is $a\pi$ , what is the value of $a$ ?

Triangle $ABC$ satisfies $2\sin B=\sin A+\sin C$ . If $a+c=30$ , what is the value of $b$ ?

Details and assumptions

$a$ , $b$ and $c$ are the lengths of the sides opposite to the vertices $A$ , $B$ and $C$ , respectively.

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Extended Sine Rule

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