Final answer:
The altitude rule and the leg rule are both rules used in trigonometry to solve right triangles. The altitude rule states that the altitude drawn from the right angle of a right triangle to the hypotenuse divides the hypotenuse into two segments. The leg rule states that in a right triangle, the length of one leg is related to the length of the other leg and the length of the hypotenuse.
Step-by-step explanation:
The altitude rule and the leg rule are both rules used in trigonometry to solve right triangles. They are based on the relationships between the sides and angles of a triangle. Here's the difference between the two:
Altitude Rule:
The altitude rule, also known as the height rule, states that the altitude drawn from the right angle of a right triangle to the hypotenuse divides the hypotenuse into two segments. The lengths of the segments are proportional to the lengths of the adjacent sides of the triangle.
For example, if we have a right triangle with sides of lengths a, b, and c (with c as the hypotenuse), and the altitude from the right angle divides the hypotenuse into segments x and y, then we have the following relationship:
a/x = x/c
where x is the length of one segment and a is the length of the adjacent side.
Leg Rule:
The leg rule, also known as the side rule, states that in a right triangle, the length of one leg is related to the length of the other leg and the length of the hypotenuse.
For example, if we have a right triangle with sides of lengths a, b, and c (with c as the hypotenuse), and a is one of the legs, then we have the following relationship:
a/b = b/c
where a is the length of one leg and b is the length of the other leg.