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To warn ships for underwater rocks, a li...

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle `80o`to a distance of 16.5 km. Find the area of the sea over which the ships are warned.

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AI Generated Solution

To find the area of the sea over which ships are warned by the lighthouse, we can use the formula for the area of a sector of a circle. The formula is: \[ \text{Area} = \frac{\theta}{360} \times \pi r^2 \] where: - \(\theta\) is the angle of the sector in degrees, ...
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To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80^@ to a distance of 16.5 km. Find the area of the sea over which the ships are warned.

To warn ships for underwater rocks, a light house throws a red coloured light over a sector of 80^o angle to a distance of 16.5 km. Find the area of the sea over which the ships are warned.

Knowledge Check

  • A cargo ship is 4.2 miles from a lighthouse, and a fishing boat is 5.0 miles from the lighthouse, as shown below. The angle between the straight lines from the lighthouse to the 3 vessels is 5^(@) . The approximate distance in miles, from the cargo ship to the fishing boat is given by which of the following expressions? (Note: The law of cosines states that for any triangle with vertices A, B and C adn the sides opposite those vertices with length a, b, and c, respectively. c^(2) = a^(2) + b^(2) - 2ab cos C ).

    A
    `sqrt((5.0)^(2) - (4.2)^(2))`
    B
    `sqrt((4.2)^(2) + (5.0)^(2) - 2 cdot 4.2 cdot 5.0 cos 5^(@))`
    C
    `sqrt((4.2)^(2) + (5.0)^(2) + 2 cdot 4.2 cdot 5.0 cos 5^(@))`
    D
    `sqrt((4.2)^(2) + (5.0)^(2) - 2 cdot 4.2 cdot 5.0 cos 85^(@))`

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