Question

In right angled $\Delta$YXZ, $\angle$X = 90^°, XZ = 8 cm, YZ = 17 cm, find sin Y, cos Y, tan Y, sin Z, cos Z, tan Z.

Answer 1

In right ∆YXZ,
YZ² = XZ² + XY² (Pythagoras theorem)
⇒ XY² = YZ² − XZ²
⇒ XY² = 17² − 8² = 289 − 64 = 225
⇒ XY² = 15²
⇒ XY = 15 cm

Now,
$\sin Y=\frac{XZ}{YZ}=\frac{8}{17}$
$\cos Y=\frac{XY}{YZ}=\frac{15}{17}$
$\tan Y=\frac{XZ}{XY}=\frac{8}{15}$

Also, $\sin Z=\frac{XY}{YZ}=\frac{15}{17}$
$\cos Z=\frac{XZ}{YZ}=\frac{8}{17}$
$\tan Z=\frac{XY}{XZ}=\frac{15}{8}$