U4 Flashcard 1 | Pyth Thrm and Sides of Trig Ratios

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). Formula: a² + b² = c².

Front

What are the three primary trigonometric functions?

Back

The three primary trigonometric functions are Sine (sin), Cosine (cos), and Tangent (tan).

Front

What is the mnemonic to remember the trigonometric ratios?

Back

Soh Cah Toa, which stands for: Soh = Sine = Opposite/Hypotenuse, Cah = Cosine = Adjacent/Hypotenuse, Toa = Tangent = Opposite/Adjacent.

Front

How do you find the length of a missing side in a right triangle?

Back

Use the Pythagorean Theorem or trigonometric ratios (sine, cosine, tangent) depending on the information given.

Front

What is the sine of an angle in a right triangle?

Back

The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the cosine of an angle in a right triangle?

Back

The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the tangent of an angle in a right triangle?

Back

The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side.

Front

If one side of a right triangle is 20 in and the hypotenuse is 80 in, what is the length of the other side?

Back

Using the Pythagorean Theorem: a² + 20² = 80²; a² + 400 = 6400; a² = 6000; a = √6000 ≈ 77.46 in.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.