Math 2: Pythagorean Theorem & Trigonometry

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: a² + b² = c².

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring 90 degrees.

Front

What are the three sides of a right triangle called?

Back

The three sides of a right triangle are called the hypotenuse (the side opposite the right angle) and the two legs (the other two sides).

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

How do you find the length of a side in a right triangle using the Pythagorean Theorem?

Back

To find the length of a side, rearrange the Pythagorean Theorem formula: c = √(a² + b²) for the hypotenuse, or a = √(c² - b²) or b = √(c² - a²) for the legs.

Front

What is the relationship between the angles in a right triangle?

Back

The sum of the angles in any triangle is always 180 degrees. In a right triangle, the two non-right angles must add up to 90 degrees.

Front

If one angle in a right triangle is 30 degrees, what is the other non-right angle?

Back

If one angle is 30 degrees, the other non-right angle must be 60 degrees, since 90 + 30 + 60 = 180.

Front

What is the value of sin(30°)?

Back

The value of sin(30°) is 1/2.