Trig and Pythagorean Theorem Review

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 is the sine function?

Back

The sine function (sin) is a trigonometric function that relates the angle of a right triangle to the ratio of the length of the opposite side to the length of the hypotenuse.

Front

What is the cosine function?

Back

The cosine function (cos) is a trigonometric function that relates the angle of a right triangle to the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

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

Back

To find the length of a side using sine, use the formula: sin(angle) = opposite/hypotenuse. Rearranging gives: opposite = hypotenuse * sin(angle).

Front

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

Back

To find the length of a side using cosine, use the formula: cos(angle) = adjacent/hypotenuse. Rearranging gives: adjacent = hypotenuse * cos(angle).

Front

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

Back

In a right triangle, the sum of the two non-right angles is always 90 degrees.

Front

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

Back

If one angle is 30 degrees, the other angle must be 60 degrees because 90 - 30 = 60.

Front

What is the length of the hypotenuse if the other two sides are 3 and 4?

Back

Using the Pythagorean Theorem: c² = 3² + 4²; c² = 9 + 16; c² = 25; c = 5.

Front

What is the sine of 90 degrees?

Back

The sine of 90 degrees is 1.