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The point B is at the centre of the circle. The pints P and Q are in the circumference of the circle. Calculate the area of the shaded sector. Take pi to be 3.142 in your working. Give your final answer to 1 dp.

The point B is at the centre of the circle The pints P and Q are in the circumference of the circle Calculate the area of the shaded sector Take pi to be 3142 i class=

Respuesta :

Answer:

24.7cm^2

Step-by-step explanation:

Line PQ = 5.413590865cm

BQ = 9cm

Angle BPQ =  

5.413590865² = 9² + 9² - 2 × 9 × 9 × cos(x)

29.30696605 = 81 + 81 - 162 × cos(x)  

29.30696605 = 162 - 162 × cos(x)

-132.693034 = -162 × cos(x)

cos(x) = 0.8190928022

x = 35.00591739˚

Area of sector = 24.7cm^2

When  point B is at the centre of the circle.  So the area of the shaded sector is 24.7 [tex]cm^2[/tex].

Calculation of the area of the shaded sector:

Since

Line PQ = 5.413590865cm

BQ = 9cm

Now

[tex]5.413590865^2 = 9^2 + 9^2 - 2 \times 9 \times 9 \times cos(x)\\\\29.30696605 = 81 + 81 - 162 \times cos(x) \\\\29.30696605 = 162 - 162 \times cos(x)\\\\-132.693034 = -162 \times cos(x)\\\\[/tex]

cos(x) = 0.8190928022

x = 35.00591739˚

Now finally the

Area of sector = 24.7cm^2

Hence, When  point B is at the centre of the circle.  So the area of the shaded sector is 24.7 [tex]cm^2[/tex].

Learn more about an area here: https://brainly.com/question/8063993