Right-Triangle Trig and Pythagorean Triples

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 can be expressed as: c² = a² + b².

Front

What are Pythagorean triples?

Back

Pythagorean triples are sets of three positive integers (a, b, c) that satisfy the Pythagorean theorem, meaning a² + b² = c². Examples include (3, 4, 5) and (5, 12, 13).

Front

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

Back

The sine of an angle (A) in a right triangle is the ratio of the length of the opposite side to the length of the hypotenuse. It is expressed as: sin A = opposite/hypotenuse.

Front

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

Back

The cosine of an angle (A) in a right triangle is the ratio of the length of the adjacent side to the length of the hypotenuse. It is expressed as: cos A = adjacent/hypotenuse.

Front

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

Back

The tangent of an angle (A) in a right triangle is the ratio of the length of the opposite side to the length of the adjacent side. It is expressed as: tan A = opposite/adjacent.

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c² = 3² + 4² = 9 + 16 = 25, so c = √25 = 5.

Front

What is the relationship between sine and cosine for complementary angles?

Back

For complementary angles A and B (where A + B = 90°), sin A = cos B and cos A = sin B.

Front

How do you find the length of a side in a right triangle using trigonometric ratios?

Back

To find a side, use the appropriate trigonometric ratio (sine, cosine, or tangent) based on the known angle and the sides involved.

Front

What is the value of sin 30°?

Back

sin 30° = 1/2.

Front

What is the value of cos 60°?

Back

cos 60° = 1/2.