Question

In the right angled $∆$XYZ, $\angle$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 1

(i) sinX = $\frac{\mathrm{Opposite}\mathrm{side}\mathrm{of}\angle \mathrm{X}}{\mathrm{Hypotenuse}}=\frac{\mathrm{YZ}}{\mathrm{XZ}}=\frac{a}{c}$

(ii) tanZ = $\frac{\mathrm{Opposite}\mathrm{side}\mathrm{of}\angle \mathrm{Z}}{\mathrm{Adjacent}\mathrm{side}\mathrm{of}\angle \mathrm{Z}}=\frac{\mathrm{XY}}{\mathrm{YZ}}=\frac{b}{a}$

(iii) cosX = $\frac{\mathrm{Adjacent}\mathrm{side}\mathrm{of}\angle \mathrm{X}}{\mathrm{Hypotenuse}}=\frac{\mathrm{XY}}{\mathrm{XZ}}=\frac{b}{c}$

(iv) tanX = $\frac{\mathrm{Opposite}\mathrm{side}\mathrm{of}\angle \mathrm{X}}{\mathrm{Adjacent}\mathrm{side}\mathrm{of}\angle \mathrm{X}}=\frac{\mathrm{YZ}}{\mathrm{XY}}=\frac{a}{b}$