In right angled ΔYXZ, ∠X = 90⁰, XZ = 8cm, YZ =17cm, find sin Y, cos Y, tan Y, sin Z, cos Z, tan Z.

For any right-angled triangle,

sinθ = Opposite side /Hypotenuse

cosθ = Adjacent side/Hypotenuse

tanθ = sinθ/cosθ

= Opposite side/Adjacent side

cotθ = 1/tanθ

= Adjacent side/Opposite side

secθ = 1/cosθ

= Hypotenuse/Adjacent side

cosecθ = 1/sinθ

= Hypotenuse/Opposite side

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

So for ∠ Y,

Opposite side = XZ =8

Adjacent side= XY

So for ∠ Z,

Opposite side = XY

Adjacent side = XZ = 8

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

So for Δ TSU,

By Pythagoras Theorem

YZ² = XZ² + XY²

XY² = 17² - 8²

= 289 - 64

= 225

XY = 15

(i) sin Y = Opposite side/Hypotenuse

= XZ/YZ

= 8/17

(ii) cos Y = Adjacent side/Hypotenuse

= XY/YZ

= 15/17

(iii) tan Y = sinθ/cosθ

= Opposite side/Adjacent side

= XZ/XY

= 8/15

(i) sin Z = Opposite side/Hypotenuse

= XY/YZ

= 15/17

(ii) cos Z = Adjacent side/Hypotenuse

= XZ/YZ

= 8/17

(iii) tan Z = sinθ/cosθ

= Opposite side/Adjacent side

= XZ/XY

= 8/15