10th ICSE maths - in chapter height and distance how we will know that in the particular question we have to use wheater sin or tan or cos.......
Answers
Answer:-
Welcome to the Concept of TRIGONOMETRY.
Trigonometry is only followed in a Right Angle Triangle.
In a Right Angle Triangle, If one of the Angle is given with its Base & we have to find Height.
Then we can use Cot or Tan.
Ex:-
Here, Angle = 60° & Base = 5cm.
& we need to find Height.
Hence,
Cot 60° = Base/Perpendicular
=> 1/√3 = 5/ x
=> x = 5√3
Hence, Height = 5√3 cm.
For Tan,
Angle = 60°
Base = 5cm
=> Tan 60° = Perpendicular/ Base
=> √3 = x/5
=> x = 5√3 cm.
Hence, Height = 5√3 cm.
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If Base is Given and we are asked to find the Length of Hypotenuse. Then we use Cos or Sec.
Ex:-
Angle = 60° & Base = 5cm.
For Cos,
Cos 60° = Base / Hypotenuse
=> 1/2 = 5/ x
=>x = 10 cm.
Hence, Hypotenuse= 10cm.
For Sec,
Sec 60° = Hypotenuse/ Base
=> 2 = x/5
=> x = 10 cm.
Hence, Hypotenuse = 10cm.
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If Hypotenuse is given & we are asked to find the Height or Vice-versa. Then we use Sin or Cosec.
Ex:-
Hypotenuse = 10cm & Angle = 60°.
For Sin,
Sin 60° = Perpendicular/ Hypotenuse
=> √3/2 = x/10
=> x= 5√3cm.
For Cosec,
Cosec 60° = Hypotenuse/ Perpendicular
=> 2/√3 = 10/x
=> x = 5√3 cm.
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Note:-
SinA = Perpendicular/Hypotenuse
Cosec A = Hypotenuse/ Perpendicular
CosA= Base/ Hypotenuse
SecA = Hypotenuse/Base
Tan A = Perpendicular/Base
CotA = Base/Perpendicular.
Hope it Helps!!
