madisonproctor
contestada

A=m/360pi times radius to the power of 2. Given the measure m of the angle and the radius r of a circle.


Find the measure of the angle if the area of the sector is 5 square centimeters and the radius is 2 centimeters. Round your answer to the nearest tenth.

Respuesta :

theleangreenbean

Area of a Sector

[tex]A=\dfrac{m}{360}*\pi r^2[/tex]

  • A = area of sector
  • m = measure of angle in degrees
  • r = radius

Solving the Question

We're given:

  • A = 5 cm²
  • r = 2 cm
  • m = ?

Plug the given information into the equation and solve for m:

[tex]A=\dfrac{m}{360}*\pi r^2\\\\5=\dfrac{m}{360}*\pi (2)^2\\\\5=\dfrac{m}{360}*4\pi \\\\\dfrac{5}{4\pi}=\dfrac{m}{360}\\\\m=\dfrac{5*360}{4\pi}\\\\m=143.2[/tex]

Answer

m = 143.2°