The base of a cube is parallel to the horizon. If the cube is cut by a plane to form a cross section, under what circumstance wo
uld it be possible for the cross section be a non-rectangular parallelogram?
2 answers:
This question has this set of answer choices:
a) when the plane cuts three faces of the cube, separating one corner from the others
b) when the plane passes through a pair of vertices that do not share a common face
c) when the plane is perpendicular to the base and intersects two adjacent vertical faces
d) when the plane makes an acute angle to the base and intersects three vertical faces
e) not enough information to answer the question
The right answer is the first choice: a) when the plane cuts three faces of the cube, separating one corner from the others
You can see a picture of this case in the figure attached: as you can see the cross section (in pink) is a triangle.
a) when the plane cuts three faces of the cube, separating one corner from the others
b) when the plane passes through a pair of vertices that do not share a common face
c) when the plane is perpendicular to the base and intersects two adjacent vertical faces
d) when the plane makes an acute angle to the base and intersects three vertical faces
e) not enough information to answer the question
The right answer is the first choice: a) when the plane cuts three faces of the cube, separating one corner from the others
You can see a picture of this case in the figure attached: as you can see the cross section (in pink) is a triangle.
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Answer:
Step-by-step explanation:
Since Segment BOA is a diameter:
Arc Ac and Arc CB are in a ratio of two to four. Since Segment BOA is a diameter, Arc ACB measures 180°. Letting the unknown value be <em>x</em>, we can write that:
Hence:
Thus, Arc CB = 120°. By the Inscribed Angle Theorem:
Therefore, ΔABC is a 30-60-90 triangle. Its sides are in the ratios shown in the image below.
Since AC is opposite from the 30° triangle, let AC = <em>a</em>.
We are given that AC = 9. Hence, <em>a</em> = 9.
BC is opposite from the 60° angle and it is given by <em>a</em>√3. Therefore:
