right angle, or defined as the longest side of a right-angled triangle, in this case h. The opposite side is the side opposite to the angle we are interested in, in this case a. The adjacent side is the side that is in contact with the angle we are interested in and the right angle, hence its name. In this case the adjacent side is b. Sine, cosine and tangent The sine of an angle is the ratio of the length of the opposite side to the length of the hypotenuse. In our case This ratio does not depend on the particular right triangle chosen, as long as it contains the angle A, since all those triangles are similar. The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse. In our case The tangent of an angle is the ratio of the length of the opposite side to the length of the adjacent side. In our case The acronym "SOH-CAH-TOA" is a useful mnemonic for these ratios. Inverse functions The inverse trigonometric functions can be used to calculate the internal angles for a right angled triangle with the length of any two sides. Arcsin can be used to calculate an angle from the length of the opposite side and the length of the hypotenuse. Arccos can be used to calculate an angle from the length of the adjacent side and the length of the hypotenuse. Arctan can be used to calculate an angle from the length of the opposite side and the length of the adjacent side. In introductory geometry and trigonometry courses, the notation sin−1, cos−1, etc., are often used in place of arcsin, arccos, etc. However, the arcsin, arccos, etc., notation is standard in higher mathematics where trigonometric functions are commonly raised to powers, as this avoids confusion between multiplicative inverse and compositional inverse. Sine, cosine and tangent rules The law of sines, or sine rule, states that the ratio of the length of a side to the sine of its corresponding opposite angle is constant, that is , where R is the radius of the circumscribed circle of the given triangle. Another interpretation of this theorem is that every triangle with angles α, β and γ is similar to a triangle with side lengths equal to sin α, sin β and sin γ. This triangle can