trig and pythagorean theorem

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.

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

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

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.

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.

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.

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

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

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

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