Trigonometry Examples

$(4.8, 9)$

Step 1

To find the $\sin (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(4.8, 9)$ , draw the triangle between the three points $(0, 0)$ , $(4.8, 0)$ , and $(4.8, 9)$ .

Opposite : $9$

Adjacent : $4.8$

Step 2

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

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Step 2.1

Raise $4.8$ to the power of $2$ .

$\sqrt{23.04 + {(9)}^{2}}$

Step 2.2

Raise $9$ to the power of $2$ .

$\sqrt{23.04 + 81}$

Step 2.3

Add $23.04$ and $81$ .

$\sqrt{104.04}$

Step 2.4

Rewrite $104.04$ as ${10.2}^{2}$ .

$\sqrt{{10.2}^{2}}$

Step 2.5

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

$10.2$

Step 3

$\sin (θ) = \frac{Opposite}{Hypotenuse}$ therefore $\sin (θ) = \frac{9}{10.2}$ .

$\frac{9}{10.2}$

Step 4

Divide $9$ by $10.2$ .

$\sin (θ) = 0.88235294$