Trigonometry Examples

$\sqrt{160^{2} + 35^{2} - 2 \cdot 160 \cdot 35 \cdot \cos (125)}$

Step 1

Raise $160$ to the power of $2$ .

$\sqrt{25600 + 35^{2} - 2 \cdot 160 \cdot 35 \cdot \cos (125)}$

Step 2

Raise $35$ to the power of $2$ .

$\sqrt{25600 + 1225 - 2 \cdot 160 \cdot 35 \cdot \cos (125)}$

Step 3

Multiply $- 2 \cdot 160 \cdot 35$ .

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Step 3.1

Multiply $- 2$ by $160$ .

$\sqrt{25600 + 1225 - 320 \cdot 35 \cdot \cos (125)}$

Step 3.2

Multiply $- 320$ by $35$ .

$\sqrt{25600 + 1225 - 11200 \cdot \cos (125)}$

Step 4

Add $25600$ and $1225$ .

$\sqrt{26825 - 11200 \cos (125)}$

Step 5

Rewrite $26825 - 11200 \cos (125)$ as $5^{2} (1073 - 448 \cos (125))$ .

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Step 5.1

Factor $25$ out of $26825$ .

$\sqrt{25 (1073) - 11200 \cos (125)}$

Step 5.2

Factor $25$ out of $- 11200 \cos (125)$ .

$\sqrt{25 (1073) + 25 (- 448 \cos (125))}$

Step 5.3

Factor $25$ out of $25 (1073) + 25 (- 448 \cos (125))$ .

$\sqrt{25 (1073 - 448 \cos (125))}$

Step 5.4

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2} (1073 - 448 \cos (125))}$

Step 6

Pull terms out from under the radical.

$5 \sqrt{1073 - 448 \cos (125)}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{1073 - 448 \cos (125)}$

Decimal Form:

$182.34323702 \dots$