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Ratios of sides of a right triangle with...

Ratios of sides of a right triangle with respect to its acute angles are known as:

A

trigonometric identities

B

trigonometry

C

trigonometric ratios of the angles

D

none of these

Text Solution

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The correct Answer is:
To solve the question regarding the ratios of sides of a right triangle with respect to its acute angles, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Right Triangle**: - A right triangle has one angle that is 90 degrees, and the other two angles are acute (less than 90 degrees). - Let's label the vertices of the triangle as A, B, and C, where angle C is the right angle. 2. **Identifying the Acute Angles**: - The two acute angles in triangle ABC are angle A and angle B. - These angles are important because the ratios of the sides of the triangle will depend on which acute angle we are considering. 3. **Defining the Sides of the Triangle**: - In a right triangle, the sides are typically referred to as: - The side opposite angle A (let's call it 'a'). - The side opposite angle B (let's call it 'b'). - The hypotenuse (the side opposite the right angle, which we can call 'c'). 4. **Understanding Trigonometric Ratios**: - The ratios of the lengths of the sides of the triangle with respect to each acute angle are known as trigonometric ratios. - For angle A: - Sine (sin A) = Opposite side / Hypotenuse = a/c - Cosine (cos A) = Adjacent side / Hypotenuse = b/c - Tangent (tan A) = Opposite side / Adjacent side = a/b - For angle B: - Sine (sin B) = Opposite side / Hypotenuse = b/c - Cosine (cos B) = Adjacent side / Hypotenuse = a/c - Tangent (tan B) = Opposite side / Adjacent side = b/a 5. **Conclusion**: - Therefore, the ratios of the sides of a right triangle with respect to its acute angles are known as **Trigonometric Ratios** of the angles. ### Final Answer: The correct answer to the question is: **Trigonometric Ratios of the Angles**.
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