Right Triangle Trigonometry

Front

What is the sine ratio in a right triangle?

Back

The sine ratio is defined as the ratio of the length of the opposite side to the length of the hypotenuse. It is expressed as: \( \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} \)

Front

What is the cosine ratio in a right triangle?

Back

The cosine ratio is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. It is expressed as: \( \cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} \)

Front

What is the tangent ratio in a right triangle?

Back

The tangent ratio is defined as the ratio of the length of the opposite side to the length of the adjacent side. It is expressed as: \( \tan(\theta) = \frac{\text{opposite}}{\text{adjacent}} \)

Front

How do you find the length of the opposite side using sine?

Back

To find the length of the opposite side, use the formula: \( \text{opposite} = \text{hypotenuse} \times \sin(\theta) \)

Front

How do you find the length of the adjacent side using cosine?

Back

To find the length of the adjacent side, use the formula: \( \text{adjacent} = \text{hypotenuse} \times \cos(\theta) \)

Front

How do you find the length of the opposite side using tangent?

Back

To find the length of the opposite side, use the formula: \( \text{opposite} = \text{adjacent} \times \tan(\theta) \)

Front

What is the Pythagorean theorem?

Back

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. It is expressed as: \( a^2 + b^2 = c^2 \)

Front

What is the relationship between sine and cosine?

Back

Sine and cosine are related through the identity: \( \sin^2(\theta) + \cos^2(\theta) = 1 \)

Front

How do you solve for an angle using sine?

Back

To solve for an angle using sine, use the inverse sine function: \( \theta = \sin^{-1}\left(\frac{\text{opposite}}{\text{hypotenuse}}\right) \)

Front

How do you solve for an angle using cosine?

Back

To solve for an angle using cosine, use the inverse cosine function: \( \theta = \cos^{-1}\left(\frac{\text{adjacent}}{\text{hypotenuse}}\right) \)