gaokao 2024 Q16

gaokao · China · beijing Sine and Cosine Rules Compute area of a triangle or related figure

In $\triangle ABC$, $a = 7$, $A$ is an obtuse angle, $\sin 2B = \frac { \sqrt { 3 } } { 7 } b \cos B$.
(1) Find $\angle A$;
(2) Choose one condition from conditions (1), (2), and (3) below as a given condition and find the area of $\triangle ABC$.
(1) $b = 7$; (2) $\cos B = \frac { 13 } { 14 }$; (3) $c \sin A = \frac { 5 } { 2 } \sqrt { 3 }$. Note: If conditions (1), (2), and (3) are solved separately, only the first solution will be graded.

In $\triangle ABC$, $a = 7$, $A$ is an obtuse angle, $\sin 2B = \frac { \sqrt { 3 } } { 7 } b \cos B$.\\
(1) Find $\angle A$;\\
(2) Choose one condition from conditions (1), (2), and (3) below as a given condition and find the area of $\triangle ABC$.\\
(1) $b = 7$; (2) $\cos B = \frac { 13 } { 14 }$; (3) $c \sin A = \frac { 5 } { 2 } \sqrt { 3 }$.\\
Note: If conditions (1), (2), and (3) are solved separately, only the first solution will be graded.

Paper Questions

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