The Shortest Distance Theorem states that the shortest distance between a point P, and a line, l, is the perpendicular line from P to l. It is also called the “perpendicular distance.” It is simple to prove this theorem using the Pythagorean Theorem.

6) may seem somewhat sudden. Rather than determining the na- ture of the function according to the calculus of variations, in this case it was already known that the cycloid is the curve of quickest descent because research on cycloids has been devel- oping for a considerable length of time.

The “c” is the hypotenuse, and although it represents the longest side of a right triangle, it is the shortest path between the two points on either end. But the hypotenuse isn’t always the shortest route. In fact, it is only the shortest one on football fields and other flat surfaces.

The trigonometry of non-right triangles So far, we’ve only dealt with right triangles, but trigonometry can be easily applied to non-right triangles because any non-right triangle can be divided by an altitude * into two right triangles.

2 Answers. The law of cosines applied to right triangles is the Pythagorean theorem, since the cosine of a right angle is 0.

Given two sides and the angle between them (SAS), find the measures of the remaining side and angles of a triangle.

1. Sketch the triangle.
2. Apply the Law of Cosines to find the length of the unknown side or angle.
3. Apply the Law of Sines or Cosines to find the measure of a second angle.

Example

1. Step 1 The two sides we know are Adjacent (6,750) and Hypotenuse (8,100).
2. Step 2 SOHCAHTOA tells us we must use Cosine.
3. Step 3 Calculate Adjacent / Hypotenuse = 6,750/8,100 = 0.8333.
4. Step 4 Find the angle from your calculator using cos-1 of 0.8333:

In a Euclidean space, the sum of measures of these three angles of any triangle is invariably equal to the straight angle, also expressed as 180 °, π radians, two right angles, or a half-turn.

180°