Right Triangles Review

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

What is a 45-45-90 triangle?

Back

A special right triangle where the angles are 45°, 45°, and 90°. The lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.

Front

How do you find the hypotenuse in a 45-45-90 triangle?

Back

Multiply the length of a leg by √2.

Front

What is the sine function 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. Formula: sin(θ) = opposite/hypotenuse.

Front

What is the cosine function 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. Formula: cos(θ) = adjacent/hypotenuse.

Front

What is the tangent function 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. Formula: tan(θ) = opposite/adjacent.

Front

What is the relationship between sine and cosine?

Back

For any angle θ, sin(θ) = cos(90° - θ). This means sine and cosine are complementary functions.

Front

What is inverse trigonometric function?

Back

Inverse trigonometric functions are used to find the angle when the values of the sides are known. Examples include sin⁻¹, cos⁻¹, and tan⁻¹.

Front

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

Back

If you know one angle (other than the right angle) and one side, you can use tan(θ) = opposite/adjacent to find the unknown side.

Front

What is the formula for finding the length of a leg in a right triangle using the Pythagorean Theorem?

Back

If you know the hypotenuse (c) and one leg (a), you can find the other leg (b) using b = √(c² - a²).