contestada

This exercise involves the formula for the area of a circular sector. the area of a sector of a circle with a central angle of 170° is 70 m2. find the radius of the circle. (round your answer to one decimal place.) m

Respuesta :

sqdancefan
The formula of interest is
A = (1/2)r²·θ
You have A = 70 m², θ = 170° = 17π/18 rad. Then the radius is found from
70 m² = (1/2)r²(17π/18)
(36·70 m²)/(17π) = r²
r ≈ √47.18476 m
r ≈ 6.9 m
VictorZ
Hi there!

• A = 70 m²
• ϴ = 170° = [tex]\dfrac {17\pi}{18}[/tex] rad.

According to th' question :-

Area of Sector = [tex]\dfrac {1}{2}[/tex]r².ϴ

70 m² = [tex]\dfrac {1}{2}[/tex]r². [tex]\dfrac {17\pi}{18}[/tex]

r² = [tex]\dfrac {36.70}{17\pi}[/tex] m²

r ≈ [tex]\sqrt {47. 18476}[/tex] m

r ≈ 6.9 m

Hence,
Th' radius of circle, r = 6.9 m


~ Hope it helps!