Precalculus Examples

$\sqrt{35^{2} + 20^{2} - 2 \cdot 35 \cdot 20 \cos (42)}$

Step 1

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

$\sqrt{1225 + 20^{2} - 2 \cdot 35 \cdot (20 \cos (42))}$

Step 2

Raise $20$ to the power of $2$ .

$\sqrt{1225 + 400 - 2 \cdot 35 \cdot (20 \cos (42))}$

Step 3

Multiply $- 2$ by $35$ .

$\sqrt{1225 + 400 - 70 \cdot (20 \cos (42))}$

Step 4

Multiply $20$ by $- 70$ .

$\sqrt{1225 + 400 - 1400 \cos (42)}$

Step 5

Add $1225$ and $400$ .

$\sqrt{1625 - 1400 \cos (42)}$

Step 6

Rewrite $1625 - 1400 \cos (42)$ as $5^{2} (65 - 56 \cos (42))$ .

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Step 6.1

Factor $25$ out of $1625$ .

$\sqrt{25 (65) - 1400 \cos (42)}$

Step 6.2

Factor $25$ out of $- 1400 \cos (42)$ .

$\sqrt{25 (65) + 25 (- 56 \cos (42))}$

Step 6.3

Factor $25$ out of $25 (65) + 25 (- 56 \cos (42))$ .

$\sqrt{25 (65 - 56 \cos (42))}$

Step 6.4

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

$\sqrt{5^{2} (65 - 56 \cos (42))}$

Step 7

Pull terms out from under the radical.

$5 \sqrt{65 - 56 \cos (42)}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$5 \sqrt{65 - 56 \cos (42)}$

Decimal Form:

$24.17844586 \dots$