Find the Tangent Given the Point (33/65,56/65)

$(\frac{33}{65}, \frac{56}{65})$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(\frac{33}{65}, \frac{56}{65})$ , draw the triangle between the three points $(0, 0)$ , $(\frac{33}{65}, 0)$ , and $(\frac{33}{65}, \frac{56}{65})$ .

Opposite : $\frac{56}{65}$

Adjacent : $\frac{33}{65}$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{\frac{56}{65}}{\frac{33}{65}}$ .

$\frac{\frac{56}{65}}{\frac{33}{65}}$

Step 3

Simplify $\tan (θ)$ .

Multiply the numerator by the reciprocal of the denominator.

$\tan (θ) = \frac{56}{65} \cdot \frac{65}{33}$

Cancel the common factor of $65$ .

Cancel the common factor.

$\tan (θ) = \frac{56}{65} \cdot \frac{65}{33}$

Rewrite the expression.

$\tan (θ) = 56 (\frac{1}{33})$

Combine $56$ and $\frac{1}{33}$ .

$\tan (θ) = \frac{56}{33}$

Step 4

Approximate the result.

$\tan (θ) = \frac{56}{33} \approx 1.\overline{69}$

Find the Tangent Given the Point (33/65,56/65)

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