Imlt09
contestada

1.) If r = 8 and the intercepted arc length is 6π, what is the measure of the central angle?

_______pi (exact answer)




2.) The measure of a central angle is 110°. The length of the radius is 15 ft. Determine the length of the intercepted arc.

_______pi (exact answer)

1 If r 8 and the intercepted arc length is 6π what is the measure of the central angle pi exact answer 2 The measure of a central angle is 110 The length of the class=

Respuesta :

oladayoademosu

1. The central angle is 3π/4

2. The length of the intercepted arc is 55π/6 ft

1.

The central angle is 3π/4

Length of an arc

The length of an arc, L = rФ where

  • r = radius of circle and
  • Ф = central angle in radians.

Central angle

Making Ф subject of the formula, we have

Ф = L/r

Since L = 6π and r = 8, substituting the values of the variables into the equation, we have

Ф = L/r

Ф = 6π/8

Ф = 3π/4

The central angle is 3π/4

2.

Length of an arc with central angle in degrees

The length of the intercepted arc is 55π/6 ft

Also, the length of an arc, L with central angle, Ф in degrees is

L = Ф/360 × 2πr where r = radius of circle

Since Ф = 110° and r = 15 ft, substituting the values of the variables into the equation, we have

L = Ф/360 × 2πr

L = 110°/360° × 2π × 15 ft

L = 11/36 × 30π ft

L = 11/6 × 5π ft

L = 55π/6 ft

The length of the intercepted arc is 55π/6 ft

Learn more about length of an arc here:

https://brainly.com/question/8402454

Otras preguntas