A field is in the shape of an equilateral tri | vedclass

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Question

(A) The field is an equilateral triangle,so each interior angle is $60^{\circ}$.The cow is tethered at one vertex,so the area it can graze is a sector

Vedclass · Accepted Answer

$13.08$

Vedclass · Answer

(A) The field is an equilateral triangle,so each interior angle is $60^{\circ}$.The cow is tethered at one vertex,so the area it can graze is a sector of a circle with radius $r = 5\, m$ and central angle $	heta = 60^{\circ}$.The formula for the area of a sector is $A = \frac{	heta}{360^{\circ}} 	imes \pi r^2$.Substituting the values: $A = \frac{60^{\circ}}{360^{\circ}} 	imes 3.14 	imes (5)^2$.$A = \frac{1}{6} 	imes 3.14 	imes 25$.$A = \frac{78.5}{6} \approx 13.0833\, m^2$.Rounding to two decimal places,the area is $13.08\, m^2$.

$A$ field is in the shape of an equilateral triangle in which the length of each side is $70\, m$. $A$ cow is tethered at one of its vertices by a $5\, m$ long rope. Find the area of the region in the field in which the cow can graze. $(\pi = 3.14)$ (in $m^2$)

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