taiwan-gsat 2025 Q8

taiwan-gsat · Other · ast__math-b 8 marks Sine and Cosine Rules Prove an inequality or ordering relationship in a triangle

On a plane, there is a triangle $A B C$ where $\angle A = 91 ^ { \circ }, \angle C = 29 ^ { \circ }$. Let $\overline { B C } = a, \overline { C A } = b, \overline { A B } = c$. Select the correct options.
(1) $a ^ { 2 } > b ^ { 2 } + c ^ { 2 }$
(2) $\frac { c } { a } > \sin 29 ^ { \circ }$
(3) $\frac { b } { a } > \cos 29 ^ { \circ }$
(4) $\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { a b } < \sqrt { 3 }$
(5) The circumradius of triangle $A B C$ is less than $c$

On a plane, there is a triangle $A B C$ where $\angle A = 91 ^ { \circ }, \angle C = 29 ^ { \circ }$. Let $\overline { B C } = a, \overline { C A } = b, \overline { A B } = c$. Select the correct options.\\
(1) $a ^ { 2 } > b ^ { 2 } + c ^ { 2 }$\\
(2) $\frac { c } { a } > \sin 29 ^ { \circ }$\\
(3) $\frac { b } { a } > \cos 29 ^ { \circ }$\\
(4) $\frac { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } { a b } < \sqrt { 3 }$\\
(5) The circumradius of triangle $A B C$ is less than $c$

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