taiwan-gsat 2022 Q11

taiwan-gsat · Other · gsat__math-a 5 marks Not Maths
The figure below is a schematic diagram of a building block, where $A B C$ is a right triangle with $\angle A C B = 90 ^ { \circ } , \overline { A C } = 5 , \overline { B C } = 6$ , and both $A D E B$ and $A D F C$ are rectangles. Select the correct options.
(1) Cutting this block along plane $A C E$ yields two tetrahedra
(2) The acute angle between planes $A D E B$ and $A D F C$ is greater than $45 ^ { \circ }$
(3) $\angle C E B < \angle A E B$
(4) $\tan \angle A E C < \sin \angle C E B$
(5) $\angle C E B < \angle A E C$
The figure below is a schematic diagram of a building block, where $A B C$ is a right triangle with $\angle A C B = 90 ^ { \circ } , \overline { A C } = 5 , \overline { B C } = 6$ , and both $A D E B$ and $A D F C$ are rectangles. Select the correct options.\\
(1) Cutting this block along plane $A C E$ yields two tetrahedra\\
(2) The acute angle between planes $A D E B$ and $A D F C$ is greater than $45 ^ { \circ }$\\
(3) $\angle C E B < \angle A E B$\\
(4) $\tan \angle A E C < \sin \angle C E B$\\
(5) $\angle C E B < \angle A E C$