Right Triangle Trigonometry

Front

What is the Pythagorean Theorem?

Back

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

How do you find the sine of an angle in a right triangle?

Back

Sine of an angle (θ) is the ratio of the length of the opposite side to the length of the hypotenuse. Formula: sin(θ) = opposite/hypotenuse.

Front

How do you find the cosine of an angle in a right triangle?

Back

Cosine of an angle (θ) is the ratio of the length of the adjacent side to the length of the hypotenuse. Formula: cos(θ) = adjacent/hypotenuse.

Front

How do you find the tangent of an angle in a right triangle?

Back

Tangent of an angle (θ) is the ratio of the length of the opposite side to the length of the adjacent side. Formula: tan(θ) = opposite/adjacent.

Front

What is the relationship between sine, cosine, and tangent?

Back

tan(θ) = sin(θ)/cos(θ). This means tangent can be expressed as the ratio of sine to cosine.

Front

What is the sine ratio for a 45-degree angle?

Back

sin(45°) = √2/2.

Front

What is the cosine ratio for a 45-degree angle?

Back

cos(45°) = √2/2.

Front

What is the tangent ratio for a 45-degree angle?

Back

tan(45°) = 1.

Front

How do you use the sine function to find a side in a right triangle?

Back

If you know an angle and the hypotenuse, use sin(θ) = opposite/hypotenuse to find the length of the opposite side.

Front

How do you use the cosine function to find a side in a right triangle?

Back

If you know an angle and the hypotenuse, use cos(θ) = adjacent/hypotenuse to find the length of the adjacent side.