Sides of a triangular field are 15 m,16m,and 17m.With the 3 corners of the field a cow ,a buffalo,and a horse are tied separately with ropes of length of 7m each to graze in the field.Find the area of the field which cannot be grazed by the 3 animals.
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se heron's formula to find the area of the triangular field ABC,
A=√s(s−a)(s−b)(s−c), where a,b,c are the side lengths of the triangle, and s=a+b+c2
⇒s=15+16+172=24,
⇒A=√24(24−15)(24−16)(24−17)=√12096=24√21 m2
x+y+z=180∘,
Area of the field which can be grazed : Ag=πr2⋅x+y+z360=π⋅72⋅180360=492π
Area of the field which can not be grazed =shaded area=As=A−Ag=24√21−492π≈3.013 m2
A=√s(s−a)(s−b)(s−c), where a,b,c are the side lengths of the triangle, and s=a+b+c2
⇒s=15+16+172=24,
⇒A=√24(24−15)(24−16)(24−17)=√12096=24√21 m2
x+y+z=180∘,
Area of the field which can be grazed : Ag=πr2⋅x+y+z360=π⋅72⋅180360=492π
Area of the field which can not be grazed =shaded area=As=A−Ag=24√21−492π≈3.013 m2
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