Question

The diagram shows a projected beam of light from the lighthouse. What is the area of water that can be covered by the light from the lighthouse? Round your answer to the nearest whole numberTo the nearest square mile, what is the area of land that can be covered by the light from the lighthouse? Round your answer to the nearest whole number

Answer 1

The problem mainly involves the area of a sector (a space formed by the radius of a circle and it's intercepted arc). The formula of finding the area of a sector is given by;

`\text{Area = }(1)/(2)\theta r2^{}`

where θ is in radian and r is the radius.

A radian is an another type of measurement of an angle, specifically it is the SI unit for measuring angles. In another words Radian's relationship to Degree is the same Meter is to Feet.

To convert a degree in to a radian we have the formla;

`\theta=degree((\pi)/(180^(\circ)))`

Therefore in our problem we must first find the angle co in degrees