Find the Tangent Given the Point (- square root of 11,5)

$(- \sqrt{11}, 5)$

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(- \sqrt{11}, 5)$ , draw the triangle between the three points $(0, 0)$ , $(- \sqrt{11}, 0)$ , and $(- \sqrt{11}, 5)$ .

Opposite : $5$

Adjacent : $- \sqrt{11}$

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{5}{- \sqrt{11}}$ .

$\frac{5}{- \sqrt{11}}$

Simplify $\tan (θ)$ .

Move the negative in front of the fraction.

$\tan (θ) = - \frac{5}{\sqrt{11}}$

Multiply $\frac{5}{\sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$\tan (θ) = - (\frac{5}{\sqrt{11}} \cdot \frac{\sqrt{11}}{\sqrt{11}})$

Combine and simplify the denominator.

Multiply $\frac{5}{\sqrt{11}}$ by $\frac{\sqrt{11}}{\sqrt{11}}$ .

$\tan (θ) = - \frac{5 \sqrt{11}}{\sqrt{11} \sqrt{11}}$

Raise $\sqrt{11}$ to the power of $1$ .

$\tan (θ) = - \frac{5 \sqrt{11}}{\sqrt{11} \sqrt{11}}$

Raise $\sqrt{11}$ to the power of $1$ .

$\tan (θ) = - \frac{5 \sqrt{11}}{\sqrt{11} \sqrt{11}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\tan (θ) = - \frac{5 \sqrt{11}}{{\sqrt{11}}^{1 + 1}}$

Add $1$ and $1$ .

$\tan (θ) = - \frac{5 \sqrt{11}}{{\sqrt{11}}^{2}}$

Rewrite ${\sqrt{11}}^{2}$ as $11$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{11}$ as $11^{\frac{1}{2}}$ .

$\tan (θ) = - \frac{5 \sqrt{11}}{{(11^{\frac{1}{2}})}^{2}}$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\tan (θ) = - \frac{5 \sqrt{11}}{11^{\frac{1}{2} \cdot 2}}$

Combine $\frac{1}{2}$ and $2$ .

$\tan (θ) = - \frac{5 \sqrt{11}}{11^{\frac{2}{2}}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$\tan (θ) = - \frac{5 \sqrt{11}}{11^{\frac{2}{2}}}$

Rewrite the expression.

$\tan (θ) = - \frac{5 \sqrt{11}}{11}$

Evaluate the exponent.

$\tan (θ) = - \frac{5 \sqrt{11}}{11}$

Approximate the result.

$\tan (θ) = - \frac{5 \sqrt{11}}{11} \approx - 1.50755672$

Find the Tangent Given the Point (- square root of 11,5)

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