CareerCup

Acute angled triangle can be formed by connecting the diagonal of three adjacent faces of the cube.
The number of ways three adjacent faces can be chosen is (6x4x2)/(3x2x1) = 8
So the total number of acute angled triangle is 8.

Easy way to think about this is start with the bottom vertex. Extend two lines from this vertex to the opposite side ( top 2 vertices ) .We have 1 acute triangle. We can repeat this process for every other vertices(which is 8). Therefore,we have 8 acute triangles.

To form an acute triangle you can only choose vertices that are not connected by an edge to each other in the cube. There are two sets of 4 such vertices (diagonals on the first face and the opposite diagonal on the bottom face). In each such set choosing any 3 would form an acute Triangle. So the answer would be 2*4C3 = 8.

0

An acute angled triangle has ALL angles less than 90*.

So yes no. of acute angles that can be formed = 8.

How do you guys come up with 8? Can you please explain?

it is 24
in every face we can form 4 acute triangles.
there are six faces...so 6*4 = 24

it is 24
in every face we can form 4 acute triangles.
there are six faces...so 6*4 = 24

please correct me if I am wrong....

Assumption: It'a an equi cube( all edges are of equal length and you can't distinguish between any two sides/edges).

The Answer is 3

1) you can select 2 vertices of an edge, and select the third vertix as one of
vertices of diognally opposite edge. (2 ways).
2) you can select 3 vertices in such a way that no two are on same edge. (only one
way)

Answer is 8

2 3
1 4

6 7
5 8
image you have a sword cut 2-4-5, which will make a acute triangle, and this can be seen as well as cutting corner 1, so how many corners that you can cut? the answer is 8

2-------3
 /       /|
1-------4 |
|       | |
| 6     | 7
|       |/
5-------8

There are total of 24 Acute Triangles in a Cube

------1--------2
3--------4

------5--------6
7--------8



(1-2-3-4)
1-4-7,----->[[1]]
1-4-6,------->[[2]]
2-3-5,--------->[[3]]
2-3-8,----------->[[4]]

(2-6-8-4)
2-8-3,----------->(4)
2-8-5,------------->[[5]]
4-6-1,------->(2)
4-6-7,----------------->[[7]]

(1-2-5-6)
1-6-7,--------------->[[6]]
1-6-4,------->(2)
2-5-3,--------->(3)
2-5-8,------------->(5)

(1-5-3-7)
1-7-4,----->(1)
1-7-6,--------------->(6)
3-5-2,--------->(3)
3-5-8,------------------->[[8]]

(3-4-7-8)
3-8-5,------------------->(8)
3-8-2,----------->(4)
4-7-1,----->(1)
4-7-6,----------------->(7)

(5-6-7-8)
6-7-1,--------------->(6)
6-7-4,----------------->(7)
5-8-2,------------->(5)
5-8-3,------------------->(8)



But, Unique Triangles are 8.

1-4-7,----->[[1]]
1-4-6,------->[[2]]
2-3-5,--------->[[3]]
2-3-8,----------->[[4]]
2-8-5,------------->[[5]]
1-6-7,--------------->[[6]]
4-6-7,----------------->[[7]]
3-5-8,------------------->[[8]]

12 diagonals
for every diagonal, 2 vertices using which an acute angle can be formed.
24 permutations in total but 8 combinations
Ans. 8

for me answer is coming 12

Total number of triangles that can be formed = 8C3 = 56
Each diagonal on each surface of the cube gives rise to 2 right angled triangles, and there are two such diagonals for each surface and 2 * 6 = 12 such diagonals
Therefore, total number of right angled triangles = 12 * 2 = 24
The rest of them are acute angled triangles i.e, 56 - 24 = 32

ans is 32.
for each edge we have 2 possibilities to choose the 3rd vertice to form a acute triangle.So 12 edges means 24 triangles.

8 other tringles can me made which does not form an edge.

i think it is 0
bcoz,in a cube when we join any 3 vertices it will always form a right angled triangle.
so,no acute angled triangle is formed.
i think so.....

Suppose x is the distance between the two poles.Now , x/2 + (15-7) should be less than 16/2 which is not possible. So the poles aren't apart

8 is the correct answer. Draw the cube, draw all possible equilateral triangles possible, eliminate the duplicates.

/|\
/ | \
/ | \
/ - |- \
\ | /
\|/
Ans 4. Think about a 3D structured triangle pyramid using 6edges.. Other 2 edges useless

12

The answer is 8 triangle.
Total number of triangles are 56. 8C3.
Now total number of Right angle triangles are 8*6. From each surface 8 right angle triangles are formed. 4 on the surface and 4 in which diagonally bottom corner is used.

So acute trianges are 56-48=8

Knimaimsismik

ans: 24 ?
total faces: 6
each face: 2 diagonals.
with each diagonal - 2 equil triangle with the diagonals of the adjacent sides to it
=> 6*2*2 = 24 !!
correct me if im wrong :)