Trigonometry: Finding Sides and Angles, Pythaogrean Theorem

Front

What is the definition of 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: \( \tan(\theta) = \frac{opposite}{adjacent} \)

Front

What is the Pythagorean Theorem?

Back

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

Front

If a right triangle has one leg measuring 6 feet and the other leg measuring 8 feet, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: \( c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \) feet.

Front

What is the definition of the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

In a right triangle, if one angle is 30 degrees, what is the ratio of the opposite side to the hypotenuse?

Back

The ratio is \( \frac{1}{2} \) for a 30-degree angle, meaning the opposite side is half the length of the hypotenuse.

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: \( \sin(\theta) = \frac{opposite}{hypotenuse} \)

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: \( \cos(\theta) = \frac{adjacent}{hypotenuse} \)

Front

If the height of a slide is 6 feet and the base is 8 feet, what is the length of the slide?

Back

Using the Pythagorean Theorem: \( c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10 \) feet.

Front

What is the opposite side in relation to an angle in a right triangle?

Back

The opposite side is the side that is directly across from the angle in question.

Front

In a right triangle, if angle C is 45 degrees, what is the relationship between the opposite and adjacent sides?

Back

For a 45-degree angle, the lengths of the opposite and adjacent sides are equal.