Find the Cosine (21,28)

$(21, 28)$

To find the $\cos (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(21, 28)$ , draw the triangle between the three points $(0, 0)$ , $(21, 0)$ , and $(21, 28)$ .

Opposite : $28$

Adjacent : $21$

Find the hypotenuse using Pythagorean theorem $c = \sqrt{a^{2} + b^{2}}$ .

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Raise $21$ to the power of $2$ .

$\sqrt{441 + {(28)}^{2}}$

Raise $28$ to the power of $2$ .

$\sqrt{441 + 784}$

Add $441$ and $784$ .

$\sqrt{1225}$

Rewrite $1225$ as $35^{2}$ .

$\sqrt{35^{2}}$

Pull terms out from under the radical, assuming positive real numbers.

$35$

$\cos (θ) = \frac{Adjacent}{Hypotenuse}$ therefore $\cos (θ) = \frac{21}{35}$ .

$\frac{21}{35}$

Cancel the common factor of $21$ and $35$ .

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Factor $7$ out of $21$ .

$\cos (θ) = \frac{7 (3)}{35}$

Cancel the common factors.

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Factor $7$ out of $35$ .

$\cos (θ) = \frac{7 \cdot 3}{7 \cdot 5}$

Cancel the common factor.

$\cos (θ) = \frac{7 \cdot 3}{7 \cdot 5}$

Rewrite the expression.

$\cos (θ) = \frac{3}{5}$

Approximate the result.

$\cos (θ) = \frac{3}{5} \approx 0.6$

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