Find the Tangent Given the Point (8/17,15/17)

$(\frac{8}{17}, \frac{15}{17})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{8}{17}, \frac{15}{17})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{8}{17}, 0)$ , and $(\frac{8}{17}, \frac{15}{17})$ .

Opposite : $\frac{15}{17}$

Adjacent : $\frac{8}{17}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{15}{17}}{\frac{8}{17}}$ .

$\frac{\frac{15}{17}}{\frac{8}{17}}$

Step 3

Simplify $\tan (θ)$ .

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{15}{17} \cdot \frac{17}{8}$

Cancel the common factor of $17$ .

Cancel the common factor.

$\tan (θ) = \frac{15}{17} \cdot \frac{17}{8}$

Rewrite the expression.

$\tan (θ) = 15 (\frac{1}{8})$

Combine $15$ and $\frac{1}{8}$ .

$\tan (θ) = \frac{15}{8}$

Step 4

Approximate the result.

$\tan (θ) = \frac{15}{8} \approx 1.875$

Find the Tangent Given the Point (8/17,15/17)

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