Angle of an arc

Watch Sal solve an example where he finds the central angle given arc length. Finding the length of an arc using the degree of the angle subtended by the arc and the perimeter of the circle. Sal finds the length of an arc using the radius and the radian measure of the angle subtended by the arc.

They are an example of coterminal angles. The zero angle (0°) and the full angle (360°) would technically look the .

Definition of the angle measure of an arc and the two ways it is written.

The length of an arc is simply the length of its portion of the circumference.

The definition of radian measure. In the diagram at the right, ∠AED is an angle formed by two intersecting chords in the circle. Notice that the intercepted arcs belong to the set of vertical angles.

Chordmalso, m∠BEC = 43º (vertical angle ) m∠CEA and m∠BED = 137º by straight angle formed. For this measurement, consider the unit circle (a circle of radius 1) whose center is the vertex of the angle in question. Then the angle cuts off an arc of the circle, and the length of that arc is the radian measure of the angle.

It is easy to convert between degree measurement and radian measurement. If you keep the above relationship in min noting where the angles go in the whole-circle formulas, you should be able to keep things straight. There are several different angles associated with circles. Perhaps the one that most immediately comes to mind is the central angle. One point to clear up: radians and degrees are measures of angles , not length.

Calculating the lengths of arcs and areas of sectors. The first step is to find the angle made by the arc or sector at the centre of the circle. Once you have done that, calculating the length of the arc or area of the sector is possible.

Remember Circumference = πd or 2πr. An arc is not always 2r, although this one happened to be equal to twice the length of the radius. The cool thing about radians as an angle measurement is that they are exactly related to the length of the radius so you can use proportions to . Sal says: Since once again they only gave us two letters, we can assume it is the minor arc . Solve problems related to radians and arc length like finding an arc length given the central angle and radius. This lesson explains how to find angle and arc measures.

The following theorems are discussed: tangent and intersected chord theorem, angles inside. The measure of an arc is the same as the degree measure of the central angle that intercepts it.