What ratio does "soh" in 'soh cah toa' remind us of?

The term "soh" in the mnemonic "soh cah toa" specifically refers to the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse. This is foundational in trigonometry when working with sine, as the sine of an angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse.

For example, if you have a right triangle where one angle measures θ, the sine function is expressed as:

sin(θ) = (length of opposite side) / (length of hypotenuse)

Therefore, "soh" effectively reminds us that whenever we calculate the sine of an angle, we are focusing on the relationship between the opposite side and the hypotenuse. This understanding is critical for solving problems related to right triangles, fractionally relating sides to angles through trigonometric functions.