Question

In a circular field, there is a rectangular tank of length 130 m and breadth 110 m. If
the area of the land portion of the field is 20350 m then find the radius of the field.
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Answer 1

Question ⤵

$\Rightarrow$ a circular field, there is a rectangular tank of length 130m and breadth 110m. If the area of the land portion of the field is 20350 m then find the radius of the field.

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Given ⤵

$\Rightarrow$ Lenght = 130 meter.

$\Rightarrow$ Breadth = 110 Meter.

Area of the tank = length × breadth

Area of the tank = 130×110

Area of the tank $\green{14,300}^{2}$

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Total area of the circular plot =20350 + 14300

= $\green{34,650}^{2}$

∴ Area of circle =$\pi {r}^{2}$ = 34650

$\frac{34650}{\pi}$ = ${r}^{2}$

$\frac{34650}{ \frac{22}{7} }$ = ${r}^{2}$

$\frac{34650 \times 7}{22}$ = ${r}^{2}$

$\frac{242,550}{22}$ = ${r}^{2}$

${r}^{2}$ = $11,025$

$r$ = $\sqrt{11025}$

$r$ = 105 meter

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Answer $\Rightarrow$ $\large\green {105}$

Answer 2

Step-by-step explanation:

1−1−cosA

1−cosA1+cosA =

= (1−cosA)(1+cosA)

= (1−cosA)(1+cosA)(1+cosA) 2 =

= sin2A

= sin2A(1+cosA) =

= (cosecA+cotA) 2

2 =∣cosecA+cotA∣

2 =∣cosecA+cotA∣=cosecA+cotA (as given)

2 =∣cosecA+cotA∣=cosecA+cotA (as given)let cosecA + cotA = x

2 =∣cosecA+cotA∣=cosecA+cotA (as given)let cosecA + cotA = xso we get |x| = x

2 =∣cosecA+cotA∣=cosecA+cotA (as given)let cosecA + cotA = xso we get |x| = xthis is possible only when x ⩾ 0

2 =∣cosecA+cotA∣=cosecA+cotA (as given)let cosecA + cotA = xso we get |x| = xthis is possible only when x ⩾ 0so cosecA + cotA ⩾ 0

2 =∣cosecA+cotA∣=cosecA+cotA (as given)let cosecA + cotA = xso we get |x| = xthis is possible only when x ⩾ 0so cosecA + cotA ⩾ 0this means that sinA > 0

2 =∣cosecA+cotA∣=cosecA+cotA (as given)let cosecA + cotA = xso we get |x| = xthis is possible only when x ⩾ 0so cosecA + cotA ⩾ 0this means that sinA > 0this is possible only in first and second quadrants