Trigonometry Examples

$\sqrt{\frac{{11.13860218}^{2} + {17.2}^{2} - {15.5}^{3}}{2 (11.13860218) (17.2)}}$

Step 1

Simplify the expression.

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Step 1.1

Raise $11.13860218$ to the power of $2$ .

$\sqrt{\frac{124.06845852 + {17.2}^{2} - {15.5}^{3}}{2 (11.13860218) (17.2)}}$

Step 1.2

Raise $17.2$ to the power of $2$ .

$\sqrt{\frac{124.06845852 + 295.84 - {15.5}^{3}}{2 (11.13860218) (17.2)}}$

Step 1.3

Raise $15.5$ to the power of $3$ .

$\sqrt{\frac{124.06845852 + 295.84 - 1 \cdot 3723.875}{2 (11.13860218) (17.2)}}$

Step 1.4

Multiply $- 1$ by $3723.875$ .

$\sqrt{\frac{124.06845852 + 295.84 - 3723.875}{2 (11.13860218) (17.2)}}$

Step 1.5

Add $124.06845852$ and $295.84$ .

$\sqrt{\frac{419.90845852 - 3723.875}{2 (11.13860218) (17.2)}}$

Step 1.6

Subtract $3723.875$ from $419.90845852$ .

$\sqrt{\frac{- 3303.96654147}{2 (11.13860218) (17.2)}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $2$ by $11.13860218$ .

$\sqrt{\frac{- 3303.96654147}{22.27720436 \cdot 17.2}}$

Step 2.2

Multiply $22.27720436$ by $17.2$ .

$\sqrt{\frac{- 3303.96654147}{383.16791499}}$

Step 3

Simplify with factoring out.

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Step 3.1

Divide $- 3303.96654147$ by $383.16791499$ .

$\sqrt{- 8.62276409}$

Step 3.2

Rewrite $- 8.62276409$ as $- 1 (8.62276409)$ .

$\sqrt{- 1 (8.62276409)}$

Step 4

Rewrite $\sqrt{- 1 (8.62276409)}$ as $\sqrt{- 1} \cdot \sqrt{8.62276409}$ .

$\sqrt{- 1} \cdot \sqrt{8.62276409}$

Step 5

Rewrite $\sqrt{- 1}$ as $i$ .

$i \sqrt{8.62276409}$