To determine the classification of the triangle based on its side lengths, we can apply the Triangle Inequality Theorem, which states that the sum of any two side lengths of a triangle must be greater than the third side length.
In this case, the shortest side is 11 cm. We can test if it forms a triangle by checking the sum of the other two sides:
19 cm + 28 cm = 47 cm
Since 47 cm is greater than 11 cm, the triangle condition is satisfied. Now, we will determine if it's acute, obtuse, or right-angled.
To determine the type of triangle based on its angles, we can use the Pythagorean Theorem, trigonometric ratios, or the Law of Cosines. Let's apply the Pythagorean theorem:
If a triangle has sides a, b, and c, with c being the longest side, then:
- If a² + b² > c², the triangle is acute.
- If a² + b² < c², the triangle is obtuse.
- If a² + b² = c², the triangle is right-angled.
Using the given side lengths:
11² + 19² = 121 + 361 = 482
28² = 784
Since 482 is less than 784, and not equal to 784, the triangle is obtuse.
Thus, the triangle with side lengths 11 cm, 19 cm, and 28 cm is classified as an obtuse triangle.
a triangle has side lengths of 11 cm, 19 cm, 28 cm. classify it as acute obtuse right or not a trianlge
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