Question

jamel is asked to create triangles using three or four given sticks. the sticks measure 3 in., 6in., 7in., and 8in. He creates these 4 triangles. how many are obtuse? 1 2 3 4

Answer 1

Answer:  He can make 3 obtuse triangle out of 4 triangles.

Step-by-step explanation:

Since, By the given numbers there can be made 4 triangles having sides:

1) 3, 6, 7

2) 6, 7, 8

3) 3, 7, 8

4) 3, 6, 8

And, for an obtuse triangle  the square of third side is always greater than the sum of two sides.

Therefore from the above four triangles only triangles 1), 3) and 4) follow the property of obtuse triangle. ( because, in triangle 1) $3^2+6^2$ , in 3) $3^2+7^2$ and in 4) $3^2+6^2$.

Thus, triangles 1), 3) and 4) are obtuse triangles.

Answer 2

There are 4 ways to choose 3 things from a set of 4:
A) 3, 6, 7
B) 3, 6, 8
C) 3, 7, 8
D) 6, 7, 8

When given 3 triangle sides, to determine if the triangle is acute, right or obtuse:

1) Square all 3 sides.

2) Sum the squares of the 2 shortest sides.

3) Compare this sum to the square of the 3rd side.

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3^2 = 9

6^2 = 36

7^2 = 49

8^2 = 64

A) 3, 6, 7
9 + 36 = 45
45 < 49
Therefore this triangle is obtuse

B) 3, 6, 8
9 + 35 = 45
45 < 64
Therefore this triangle is obtuse

C) 3, 7, 8
9 + 49 = 58
58 < 64
Therefore this triangle is obtuse

D) 6, 7, 8
36 + 49 = 85
85 > 64
Therefore this triangle is acute

So, 3 of the 4 triangles are obtuse.

Source:
http://www.1728.org/triantest.htm