Q. 33.8( 19 Votes )

In right angled Δ

Answer :

For any right-angled triangle,

sinθ = Opposite side Side/Hypotenuse


cosθ = Adjacent sideSide/Hypotenuse


tanθ = sinθ/cosθ


= Opposite side Side/Adjacent sideSide


cotθ = 1/tanθ


= Adjacent sideSide/Opposite side Side


secθ = 1/cosθ


= Hypotenuse/Adjacent sideSide


cosecθ = 1/sinθ


= Hypotenuse/Opposite side Side


In the given triangle let us understand, the Opposite side and Adjacent sidesides.


So for 50°,


Opposite side Side = MN


Adjacent sideSide = LM


So for 40°,


Opposite side Side = LM


Adjacent sideSide = MN


In general, for the side Opposite side to the 90° angle is the hypotenuse.


So, for Δ LMN, hypotenuse = LN


(i) sin 50° = Opposite side Side/Hypotenuse


= MN/LN


(ii) cos 50° = Adjacent sideSide/Hypotenuse


= LM/LN


(iii) tan 40° = sinθ/cosθ


= Opposite side Side/Adjacent sideSide


= LM/MN


(iv) cos 40° = Adjacent sideSide/Hypotenuse


= MN/LN


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