Suppose that a triangle has side lengths of 10, 11, and 17. Is the triangle as acute, obtuse, or right? How do you know? Explain.

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Suppose that a triangle has side lengths of 10, 11, and 17. Is the triangle as acute, obtuse, or right? How do you know? Explain.

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Answer 1 · 2017-12-08T08:56:59

This is an Obtuse Triangle

Explanation:

Start by calculating the squares of each side. We know that if sum of squares of two smaller sides equal the largest side, it is a right triangle (Pythagoras theorem).

$10^{2} = 100$ $10^2 = 100$
$11^{2} = 121$ $11^2 = 121$
$17^{2} = 289$ $17^2 = 289$

We note that $100 + 121 = 221 < 289$ $100+121=221 < 289$ , this is a property of an obtuse triangle.

Following is a general rule for a triangle with three sides, $a, b, c$ $a,b,c$ , where $a \leq b \leq c$ $a\leb\lec$ .

Right Triangle $\Rightarrow a^{2} + b^{2} = c^{2}$ $=> a^2+b^2 = c^2$
Acute Triangle $\Rightarrow a^{2} + b^{2} > c^{2}$ $=> a^2+b^2 > c^2$
Obtuse Triangle $\Rightarrow a^{2} + b^{2} < c^{2}$ $=> a^2+b^2 < c^2$

You can verify it by trying an equilateral triangle (which is an acute triangle), $a = 1, b = 1, c = 1$ $a = 1, b= 1, c=1$

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Suppose that a triangle has side lengths of 10, 11, and 17. Is the triangle as acute, obtuse, or right? How do you know? Explain.

1 Answer

Explanation:

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