Geom Ch 9 Review for Test

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 height of a ladder leaning against a wall?

Back

Use the sine ratio: \( \text{height} = \text{length of ladder} \times \sin(\theta) \), where \( \theta \) is the angle between the ladder and the ground.

Front

How do you find the distance from the wall to the base of the ladder?

Back

Use the cosine ratio: \( \text{distance} = \text{length of ladder} \times \cos(\theta) \), where \( \theta \) is the angle between the ladder and the ground.

Front

What is the Pythagorean theorem?

Back

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: \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse.

Front

If a ladder is 15 feet long and 9 feet away from the wall, how high does it reach?

Back

Use the Pythagorean theorem: \( h = \sqrt{15^2 - 9^2} = 12 \text{ ft} \)

Front

If a ladder makes a 40° angle with the floor and is 12 feet long, how high does it reach?

Back

Use the sine ratio: \( h = 12 \times \sin(40°) \approx 7.7 \text{ ft} \)

Front

What is the formula to calculate the height of an object using trigonometry?

Back

Height can be calculated using: \( \text{Height} = \text{Distance} \times \tan(\theta) \) for angles in right triangles.

Front

What is the relationship between angles and sides in a right triangle?

Back

The angles determine the ratios of the sides, which can be expressed using sine, cosine, and tangent functions.