Trigonometry Missing Side

Front

What is the definition of 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

How do you find the length of a missing side in a right triangle?

Back

To find the length of a missing side, use the Pythagorean theorem if two sides are known, or trigonometric ratios (sine, cosine, tangent) if an angle and one side are known.

Front

What is the sine ratio 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 ratio 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 ratio 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

If one side of a right triangle is 5 and the other is 12, what is the length of the hypotenuse?

Back

Using the Pythagorean theorem: c² = 5² + 12²; c² = 25 + 144; c² = 169; c = 13.

Front

How do you round a number to the nearest tenth?

Back

To round a number to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.

Front

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

Back

In a right triangle, the larger the angle, the longer the opposite side. The sum of the angles in any triangle is always 180 degrees.

Front

If the hypotenuse of a right triangle is 10 and one side is 6, what is the length of the other side?

Back

Using the Pythagorean theorem: c² = a² + b²; 10² = 6² + b²; 100 = 36 + b²; b² = 64; b = 8.