Right Triangle Trig

Front

What is a right triangle?

Back

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

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): c² = a² + b².

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

What are the sine, cosine, and tangent ratios?

Back

Sine (sin) = opposite/hypotenuse, Cosine (cos) = adjacent/hypotenuse, Tangent (tan) = opposite/adjacent.

Front

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

Back

To find the sine of an angle, divide the length of the side opposite the angle by the length of the hypotenuse.

Front

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

Back

To find the cosine of an angle, divide the length of the side adjacent to the angle by the length of the hypotenuse.

Front

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

Back

To find the tangent of an angle, divide the length of the side opposite the angle by the length of the side adjacent to the angle.

Front

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

Back

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

Front

If one leg of a right triangle is 6 cm and the other leg is 8 cm, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c² = 6² + 8²; c² = 36 + 64; c² = 100; c = 10 cm.

Front

What is the sine of angle A if the opposite side is 5 and the hypotenuse is 13?

Back

sin A = opposite/hypotenuse = 5/13.