Q. 24.3( 19 Votes )

# In the right angled ΔXYZ, ∠XYZ = 90^{0} 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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