A bird caught a fish on the waters surface and flew in a straight line diagonal to the water for 100 yards. Then, it dropped the fish straight down. The fish landed at a spot 50 yards away horizontally from the point where the bird caught it.
The bird flies at an angle of degrees from the water, and its height from the ground when it drops the fish is yards.
Answers
The bird flies at an angle of 60° &
Height from where fish was dropped is 50√3 yards
The above stated situation can be drawn in following way (see diagram)
In triangle ABC
BC = Distance from where fish was picked and dropped
BC = 50 yards
AC = Distance that bird flew diagonally catching the fish
AC = 100 yards
AB = Height from where fish was dropped
Now, Cos C = B/H = BC/AC
Cos C = 50/100
Cos C = 1/2
C = 60°______(1)
The bird flies at an angle of 60°
Now, sin60° = AB/AC
√3/2 = AB/100
AB = 50√3 yards
Height from where fish was dropped is 50√3 yards
60° is the angle & 86.6 yard is the height
Step-by-step explanation:
Bird flew in a straight line diagonal to the water for 100 yards
The fish landed at a spot 50 yards away horizontally from the point where the bird caught it.
Let say angle at which bird fly = α
Cosα = 50/100
=> Cosα = 1/2
=> α = 60°
The bird flies at an angle of 60°
height from the ground when it drops the fish is yards. = h
=> h² = 100² - 50²
=> h² = (100 + 50)(100 - 50)
=> h² = 150 * 50
=> h = 50√3
=> h = 86.6 Yards
height from the ground when it drops the fish is 86.6 Yards
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