Standing at one corner of a square piece of land, a boy looks in the diagonally opposite direction and sees an object that looks like a scare crow. At the moment his angle of elevation formed is 60°. He starts walking back home in a straight line and after 80 ft realizes that the angle of elevation of the object now is only 30°. Find the area of the land he was standing on
Answer with explanationAnswer: Option B
|Tan 60° = 3 =||PQ|
∴ PQ = 3 QR
|Tan 30° =||1||=||PQ||=||PQ|
∴ 80 + QR = 3 PQ
∴ 80 + QR = 3QR
∴ QR = 40 ft.
If we read carefully, we see that the boy (Point R) and the scarecrow (Point Q) are in diagonally opposite corners.
So QR is a diagonal of the square farm.
Diagonal of square = side x 2
∴ 40 = side x 2
∴ side = 40/2
∴ Area = (side)2 = (40/2)2 = (1600/2) = 800sq.ft.