A farmer has a circular piece of land．He wishes to construct his house in the form of largest possible square within the land as shown below． $\bullet \bullet \bullet \bullet$ The radius of circular piece of land is 35 m . Based on given information, answer the following questions : i Find the length of wire needed to fence the entire land. ii Find the length of each side of the square land on which house will be constructed. iii The farmer wishes to grow grass on the shaded region around the house. Find the cost of growing the grass at the rate of ₹ 50 per square metre. iiv Find the ratio of area of land on which house is built to remaining area of circular piece of land.
Explanation
To find the length of the stairs, we can use the sine function. Let's call the length of the stairs 'l'. We know that the height of the door sill is 15 feet and the angle is 60°. So, we can form a right triangle with the height as the opposite side and the length as the hypotenuse. The sine of the angle 60° is equal to the opposite side divided by the hypotenuse, which is 15/l = √3/2. Solving for l, we get l = 15√3.
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