Question

In right angled $∆$TSU, TS = 5, $\angle$S = 90^°, SU = 12 then find sin T, cos T, tan T. Similarly find sin U, cos U, tan U.

Answer 1

In right ∆TSU,

TU² = SU² + TS² (Pythagoras theorem)

⇒ TU² = 12² + 5² = 144 + 25 = 169

⇒ TU² = 13²

⇒ TU = 13

Now,

$$\begin{gathered} \mathrm{sinT}=\frac{\mathrm{SU}}{\mathrm{TU}}=\frac{12}{13} \\ \mathrm{cosT}=\frac{\mathrm{TS}}{\mathrm{TU}}=\frac{5}{13} \\ \mathrm{tanT}=\frac{\mathrm{SU}}{\mathrm{TS}}=\frac{12}{5} \end{gathered}$$
Also,

$$\begin{gathered} \mathrm{sinU}=\frac{\mathrm{TS}}{\mathrm{TU}}=\frac{5}{13} \\ \mathrm{cosU}=\frac{\mathrm{SU}}{\mathrm{TU}}=\frac{12}{13} \\ \mathrm{tanU}=\frac{\mathrm{TS}}{\mathrm{SU}}=\frac{5}{12} \end{gathered}$$