How to find opposite, adjacent, hypotenuse examples

📚 Quick Study Guide

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• Right Triangles: The opposite, adjacent, and hypotenuse are always defined with respect to a specific acute angle in a right triangle.
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• Hypotenuse: The side opposite the right angle; it's the longest side of the right triangle.
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• Opposite: The side opposite to the angle of interest.
Adjacent: The side next to the angle of interest (that is not the hypotenuse). ➗
• Trigonometric Ratios: These sides are used to define sine, cosine, and tangent: $\sin(\theta) = \frac{\text{Opposite}}{\text{Hypotenuse}}$, $\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$, $\tan(\theta) = \frac{\text{Opposite}}{\text{Adjacent}}$.

Practice Quiz

1. Which side is always the longest in a right triangle?
   1. Opposite
   2. Adjacent
   3. Hypotenuse
   4. Base
2. With respect to angle A in a right triangle, which side is directly across from it?
   1. Adjacent
   2. Hypotenuse
   3. Opposite
   4. Base
3. In a right triangle, if the hypotenuse is 13 and one leg is 5, what could be the length of the adjacent side to the angle opposite the side with length 5?
   1. 8
   2. 12
   3. 18
   4. √194
4. Which trigonometric ratio uses the opposite and hypotenuse?
   1. Cosine
   2. Tangent
   3. Sine
   4. Cotangent
5. Identify the adjacent side to angle θ in a right triangle where the hypotenuse is 10 and the opposite side is 6.
   1. 6
   2. 10
   3. 8
   4. 16
6. In a right triangle ABC, where C is the right angle, which side is adjacent to angle A?
   1. BC
   2. AC
   3. AB
   4. Cannot be determined
7. If \(\sin(\theta) = \frac{3}{5}\), which side corresponds to the number 3?
   1. Hypotenuse
   2. Adjacent
   3. Opposite
   4. Base