In the right angled ∆XYZ, ∠XYZ = 90° and a, b, c are the lengths

1.	In the right angled ∆XYZ, ∠XYZ = 90° 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» i. sin X = \(\cfrac{Opposite \,side \,of ∠ X}{Hypotenuse}\) = \(\frac{YZ}{XZ}\) = \(\frac{a}{c}\) ii. tan Z = \(\cfrac{Opposite \,side \,of ∠ Z}{Adjaent \,side \,of \, ∠ Z}\) = \(\frac{XY}{YZ}\) = \(\frac{b}{a}\) iii. cos X = \(\cfrac{Adjacent \,side \,of ∠ X}{Hypotenuse}\) = \(\frac{XY}{XZ}\) = \(\frac{b}{c}\) ii. tan X = \(\cfrac{Opposite \,side \,of ∠ X}{Adjaent \,side \,of \, ∠ X}\) = \(\frac{XZ}{XY}\) = \(\frac{a}{b}\)

In the right angled ∆XYZ, ∠XYZ = 90° 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»

i. sin X = \(\cfrac{Opposite \,side \,of ∠ X}{Hypotenuse}\) = \(\frac{YZ}{XZ}\) = \(\frac{a}{c}\)

ii. tan Z = \(\cfrac{Opposite \,side \,of ∠ Z}{Adjaent \,side \,of \, ∠ Z}\) = \(\frac{XY}{YZ}\) = \(\frac{b}{a}\)

iii. cos X = \(\cfrac{Adjacent \,side \,of ∠ X}{Hypotenuse}\) = \(\frac{XY}{XZ}\) = \(\frac{b}{c}\)

ii. tan X = \(\cfrac{Opposite \,side \,of ∠ X}{Adjaent \,side \,of \, ∠ X}\) = \(\frac{XZ}{XY}\) = \(\frac{a}{b}\)