Find the Tangent Given the Point (20,-15)

$(20, - 15)$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(20, - 15)$ , draw the triangle between the three points $(0, 0)$ , $(20, 0)$ , and $(20, - 15)$ .

Opposite : $- 15$

Adjacent : $20$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{- 15}{20}$ .

$\frac{- 15}{20}$

Step 3

Simplify $\tan (θ)$ .

Cancel the common factor of $- 15$ and $20$ .

Factor $5$ out of $- 15$ .

$\tan (θ) = \frac{5 (- 3)}{20}$

Cancel the common factors.

Factor $5$ out of $20$ .

$\tan (θ) = \frac{5 \cdot - 3}{5 \cdot 4}$

Cancel the common factor.

$\tan (θ) = \frac{5 \cdot - 3}{5 \cdot 4}$

Rewrite the expression.

$\tan (θ) = \frac{- 3}{4}$

Move the negative in front of the fraction.

$\tan (θ) = - \frac{3}{4}$

Step 4

Approximate the result.

$\tan (θ) = - \frac{3}{4} \approx - 0.75$

Find the Tangent Given the Point (20,-15)

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