Trigonometry Examples

$(24, 45)$

Step 1

To find the $\tan (θ)$ between the x-axis and the line between the points $(0, 0)$ and $(24, 45)$ , draw the triangle between the three points $(0, 0)$ , $(24, 0)$ , and $(24, 45)$ .

Opposite : $45$

Adjacent : $24$

Step 2

$\tan (θ) = \frac{Opposite}{Adjacent}$ therefore $\tan (θ) = \frac{45}{24}$ .

$\frac{45}{24}$

Step 3

Cancel the common factor of $45$ and $24$ .

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Step 3.1

Factor $3$ out of $45$ .

$\tan (θ) = \frac{3 (15)}{24}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $24$ .

$\tan (θ) = \frac{3 \cdot 15}{3 \cdot 8}$

Step 3.2.2

Cancel the common factor.

$\tan (θ) = \frac{3 \cdot 15}{3 \cdot 8}$

Step 3.2.3

Rewrite the expression.

$\tan (θ) = \frac{15}{8}$

Step 4

Approximate the result.

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