Question
How many triangles can be made? If two sides are 4 inches and the angle between them is 90°
Answers
Answered by
GPT 3.5
In order to determine the number of triangles that can be made, we need to know the length of the third side.
If the third side is less than the difference between the two sides (4 inches), a triangle cannot be formed.
If the third side is greater than the difference between the two sides (4 inches), a triangle can be formed.
Given that the angle between the two sides is 90°, and one side is 4 inches, we can use the Pythagorean theorem to find the length of the third side.
Using the Pythagorean theorem: c^2 = a^2 + b^2, where c is the hypothenuse (third side) and a and b are the two other sides.
In this case, c^2 = 4^2 + 4^2 = 16 + 16 = 32.
Hence, c = √32 ≈ 5.66 inches.
Therefore, if the third side is greater than 4 inches and less than 5.66 inches, a triangle can be formed.
So, the number of triangles that can be made with two sides measuring 4 inches and an angle of 90° between them is infinite because there is an infinite number of lengths that satisfy the condition of being greater than 4 inches and less than 5.66 inches.
If the third side is less than the difference between the two sides (4 inches), a triangle cannot be formed.
If the third side is greater than the difference between the two sides (4 inches), a triangle can be formed.
Given that the angle between the two sides is 90°, and one side is 4 inches, we can use the Pythagorean theorem to find the length of the third side.
Using the Pythagorean theorem: c^2 = a^2 + b^2, where c is the hypothenuse (third side) and a and b are the two other sides.
In this case, c^2 = 4^2 + 4^2 = 16 + 16 = 32.
Hence, c = √32 ≈ 5.66 inches.
Therefore, if the third side is greater than 4 inches and less than 5.66 inches, a triangle can be formed.
So, the number of triangles that can be made with two sides measuring 4 inches and an angle of 90° between them is infinite because there is an infinite number of lengths that satisfy the condition of being greater than 4 inches and less than 5.66 inches.
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