. When fresh fish is dried, it becomes 1/3 of its weight. If we want 6 kg dried fish, how much kilograms of fresh fish is needed?
Answers
Answer:
✯ Given :-
Two poles of equal heights are standing opposite each other on either sides of the road, which is 80 m wide.
From a point between them on the road, the angles of elevation of the top of the poles are 60° and 30° respectively.
✯ To Find :-
What is the height of the poles and the distance of the point from the poles.
✯ Solution :-
» Let, AD and BC be two poles of equal heights h m.
» And, P be a point on the road such that AP = x m, BP = (80 - x) m.
» Given that, ∠APD = 60°, ∠BPC = 30°
➙ In the ∆APD, we have,
⇒ tan60° = \dfrac{AD}{AP}
AP
AD
⇒ √3 = \dfrac{h}{x}
x
h
⇒ x = \dfrac{h}{√3}
√3
h
..... Equation no (1)
➙ In the ∆BPC we have,
⇒ tan30° = \dfrac{BC}{BP}
BP
BC
⇒ \dfrac{1}{√3}
√3
1
= \dfrac{h}{80 - x}
80−x
h
⇒ 80 - x = √3h
⇒ x = 80 - √3h .... Equation no (2)
➣ By solving the equation no (1) and (2) we get,
⇒ \dfrac{h}{√3}
√3
h
= 80 - √3 h
⇒ h = √3 (80 - √3h)
⇒ h = 80√3 - 3h
⇒ 4h = 80√3
⇒ h = \sf\dfrac{\cancel{80√3}}{\cancel{4}}
4
80√3
\dashrightarrow⇢ h = 20√3
➣ Putting h = 20√3 in the equation no (1) we get,
⇒ x = \dfrac{h}{√3}
√3
h
⇒ x = \dfrac{20√3}{√3}
√3
20√3
➠ x = 20 m
⋆ And,
AP = x = 20 m
BP = 80 - x = 80 - 20 = 60 m
\therefore∴ The height of the poles is 20√3 m .
\therefore∴ The distance of the point from the poles is 20 m and 60 m .
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