In right angled ΔTSU, TS = 5, ∠S = 90⁰, SU =12 then find sin T, cos T, tan T. Similarly find sin U, cos U, tan U.

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 ∠ T,

Opposite side= US =12

Adjacent side = TS = 5

So for ∠ U,

Opposite side = TS = 5

Adjacent side = US = 12

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

So for Δ TSU,

By Pythagoras Theorem

Hypotenuse² = Opposite side² + Adjacent²

= 12² + 5²

= 144 + 25

= 169

Hypotenuse = 13

(i) sin T = Opposite side/Hypotenuse

= US/TU

= 12/13

(ii) cos T= Adjacent side/Hypotenuse

= TS/TU

= 5/13

(iii) tan T = sinθ/cosθ

= Opposite side/Adjacent side

= US/TS

= 12/5

(i) sin U = Opposite side/Hypotenuse

= TS/TU

= 5/13

(ii) cos T= Adjacent side/Hypotenuse

= US/TU

= 12/13

(iii) tan T = sinθ/cosθ

= Opposite side /Adjacent side

= TS/US

= 5/12