Laws of Sine and Cosine

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Review the Laws of Sine and Cosine

1 : This first problem is set written so that there is no ambiguity in the use of the Law of Sines and each triangle is uniquely determined by the information given. We will continue to use our established naming convention for angles and the sides they are opposite from.

(a): Suppose $\alpha = \sage {Alpha1a}, \beta = \sage {Beta1a},$ and $A=\sage {A1a}$ . Find $B$ . $B = \answer {\sage {B1a}}$
(b): Suppose $\alpha = \sage {Alpha1b}, \gamma = \sage {Gamma1b},$ and $B=\sage {B1b}$ . Find $C$ . $C = \answer {\sage {C1b}}$
(c): Suppose $\alpha = \sage {Alpha1c}, \beta = \sage {Alpha1c},$ and $C = \sage {C1c}$ . Since the sides opposite equal angles are equal, we have that $A=B$ . Find $A$ and $B$ . $A = B = \answer {\sage {A1c}}$

2 :

(a): Suppose $\gamma = \sage {Gamma2a}, A=\sage {A2a}$ and $B=\sage {B2a}$ . Find $C$ . $C = \answer {\sage {C2a}}$
(b): Suppose $\beta = \sage {Beta2b}, A=\sage {A2b}$ and $C=\sage {C2b}$ . Find $B$ . $B = \answer {\sage {B2b}}$
(c): Suppose $A = \sage {A2c}, B = \sage {B2c},$ and $C=\sage {C2c}$ . Find $\beta$ . $\beta = \answer {\sage {Beta2c}}$
(d): Suppose $A = \sage {A1d}, B = \sage {A1d},$ and $C=\sage {C1d}$ . Find $\gamma$ . $\gamma = \answer {\sage {Gamma1d}}$