Find the Tangent Given the Point (80/89,39/89)

$(\frac{80}{89}, \frac{39}{89})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{80}{89}, \frac{39}{89})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{80}{89}, 0)$ , and $(\frac{80}{89}, \frac{39}{89})$ .

Opposite : $\frac{39}{89}$

Adjacent : $\frac{80}{89}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{39}{89}}{\frac{80}{89}}$ .

$\frac{\frac{39}{89}}{\frac{80}{89}}$

Step 3

Simplify $\tan (θ)$ .

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{39}{89} \cdot \frac{89}{80}$

Cancel the common factor of $89$ .

Cancel the common factor.

$\tan (θ) = \frac{39}{89} \cdot \frac{89}{80}$

Rewrite the expression.

$\tan (θ) = 39 (\frac{1}{80})$

Combine $39$ and $\frac{1}{80}$ .

$\tan (θ) = \frac{39}{80}$

Step 4

Approximate the result.

$\tan (θ) = \frac{39}{80} \approx 0.4875$

Find the Tangent Given the Point (80/89,39/89)

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