Q. 24.3( 19 Votes )

In the right angled ΔXYZ, XYZ = 900 and a,b,c are the lengths of the sides as shown in the figure. Write the following ratios,

(i) sin X (ii) tan Z

(iii) cos X (iv) tan X.


Answer :

For any right-angled triangle,

sinθ = Opposite side Side/Hypotenuse


cosθ = Adjacent Side/Hypotenuse


tanθ = sinθ/cosθ


= Opposite Side/Adjacent Side



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


So for X,


Opposite Side = YZ = a


Adjacent Side = XY = b


So for Z,


Opposite  Side = XY = b


Adjacent Side = YZ = a


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


So for Δ XYZ, hypotenuse = XZ = c


(i) sin X = Opposite side Side/Hypotenuse


= YZ/XZ


= a/c


(ii) tan Z = sinθ/cosθ


= Opposite  Side/Adjacent Side


= XY/YZ


= b/a


(iii) cos X= Adjacent  Side/Hypotenuse


= XY/XZ


= b/c


(iv) tan X = sinθ/cosθ


= Opposite  Side/Adjacent Side


= YZ/XY


= a/b

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