A triangle has sides A, B, and C. Sides A and B are of lengths $9$ $9$ and $7$ $7$ , respectively, and the angle between A and B is $\frac{π}{2}$ $(pi)/2$ . What is the length of side C?

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A triangle has sides A, B, and C. Sides A and B are of lengths $9$ $9$ and $7$ $7$ , respectively, and the angle between A and B is $\frac{π}{2}$ $(pi)/2$ . What is the length of side C?

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Answer 1 · 2016-02-20T21:05:06

C = $\sqrt{130} \approx 11.4$ $sqrt130 ≈ 11.4$

Explanation:

Since the angle between A and B is $\frac{π}{2} then this is a right triangle with C , the hypotenuse.$ $pi/2 " then this is a right triangle with C , the hypotenuse."$

hence C, can be found using $Pythagoras' Theorem$ $color(blue)" Pythagoras' Theorem"$

$C^{2} = A^{2} + B^{2} \Rightarrow C^{2} = 9^{2} + 7^{2} = 81 + 49 = 130$ $C^2 = A^2 + B^2 rArr C^2 = 9^2 + 7^2 = 81 + 49 = 130$

$\Rightarrow C = \sqrt{130} \approx 11.4$ $rArr C = sqrt130 ≈ 11.4$

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A triangle has sides A, B, and C. Sides A and B are of lengths $9$ $9$ and $7$ $7$ , respectively, and the angle between A and B is $\frac{π}{2}$ $(pi)/2$ . What is the length of side C?

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A triangle has sides A, B, and C. Sides A and B are of lengths $9$ $9$ and $7$ $7$ , respectively, and the angle between A and B is $\frac{π}{2}$ $(pi)/2$ . What is the length of side C?