Question
In terms of the sides of a right triangle, how would you express \( \tan(\theta) \)?
Ask by Elliott Reese. in South Africa
Dec 28,2024
Real Tutor Solution
Tutor-Verified Answer
Answer
\( \tan(\theta) \) is the ratio of the opposite side to the adjacent side in a right triangle, so \( \tan(\theta) = \frac{a}{b} \).
Solution
In a right triangle, the tangent of an angle \( \theta \) is defined as the ratio of the length of the opposite side to the length of the adjacent side.
Mathematically, this can be expressed as:
\[
\tan(\theta) = \frac{a}{b}
\]
where:
- \( a \) is the length of the side opposite the angle \( \theta \),
- \( b \) is the length of the side adjacent to the angle \( \theta \).
This relationship is fundamental in trigonometry and is used to relate the angles and sides of right triangles.
Reviewed and approved by the UpStudy tutoring team
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In a right triangle, the tangent of an angle \( \theta \) is expressed as the ratio of the length of the opposite side to the length of the adjacent side. So, \( \tan(\theta) = \frac{\text{Opposite Side}}{\text{Adjacent Side}} \). It's like a little secret handshake in geometry that helps you navigate the triangle! When using this ratio in real life, think of it as a practical tool for elevation. If you're climbing a hill and want to know how steep it is compared to how far you've walked across the base, the tangent can give you that angle. This is commonly used in navigation, architecture, and even in everyday decision-making when dealing with inclines!
