trig and pythagorean theorem

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 hypotenuse of a right triangle?

Back

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

Front

What is the sine function?

Back

The sine function (sin) 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) relates the angle of a right triangle to the ratio of the length of the adjacent side to the length of the hypotenuse.

Front

What is the tangent function?

Back

The tangent function (tan) relates the angle of a right triangle to 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 missing side in a right triangle?

Back

You can use the Pythagorean Theorem (a² + b² = c²) or trigonometric functions (sin, cos, tan) depending on the information given.

Front

If one side of a right triangle is 12 cm and the hypotenuse is 15 cm, what is the length of the other side?

Back

Using the Pythagorean Theorem: a² + 12² = 15²; a² + 144 = 225; a² = 81; a = 9 cm.

Front

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

Back

The larger the angle, the longer the opposite side. The smallest angle is opposite the shortest side.

Front

What is the formula to calculate the distance from the base of a wall to the base of a ladder leaning against it?

Back

Use the Pythagorean Theorem: distance² + height² = ladder length².