What is the tangent ratio of angle x?
Understand the Problem
The question is asking for the tangent ratio, which is a trigonometric function that can be calculated based on the lengths of the sides of a right triangle relative to angle x. Specifically, the tangent of an angle is defined as the ratio of the opposite side to the adjacent side.
Answer
$$ \tan(x) = \frac{a}{b} $$
Answer for screen readers
The tangent ratio is calculated as: $$ \tan(x) = \frac{a}{b} $$
Steps to Solve
- Identify the sides of the right triangle
To find the tangent ratio, first identify the lengths of the sides of the triangle related to angle $x$. You will need the length of the opposite side and the length of the adjacent side.
- Write the tangent ratio equation
The tangent of angle $x$, denoted as $\tan(x)$, is defined by the formula: $$ \tan(x) = \frac{\text{opposite}}{\text{adjacent}} $$
- Substitute the values into the equation
Replace the "opposite" and "adjacent" in the equation with their respective lengths. If the opposite side has a length of $a$ and the adjacent side has a length of $b$, the equation will become: $$ \tan(x) = \frac{a}{b} $$
- Compute the tangent ratio
Perform the division to find the value of the tangent ratio.
The tangent ratio is calculated as: $$ \tan(x) = \frac{a}{b} $$
More Information
The tangent function is crucial in trigonometry and is often used in calculating angles or distances in various applications, such as physics and engineering.
Tips
- Mixing up the opposite and adjacent sides. Always ensure you identify the correct sides relative to the angle in question.
- Forgetting to simplify the ratio if possible or not performing the division accurately.
