Question

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


anyone present then answer fast..!!
​

Answer 1

Corrected question:

In a right-angled ∆TSU, TS = 5, angle S = 90°, SU = 12 then find sinT, cosT, tanT. Similarly find sinU, cosU, tanU.

‎

Answers:

• sinT = 12/13

• cosT = 5/13

• tanT = 12/5

• sinU = 5/13

• cosU = 12/13

• tanU = 5/12

‎

Step-by-step explanation:

In ΔTSU:

∠TSU = 90°, On applying Pythagoras' theorem we get:

‎

⇒ Hypotenuse² = Altitude² + Base²

⇒ TU² = TS² + SU²

⇒ TU² = (5)² + (12)²

⇒ TU² = 25 + 144

⇒ TU² = 169

⇒ TU = √169

⇒ TU = ±13

Lengths can't be negative, therefore TU = 13.

‎

Now, we'll have to find the values of sinT, cosT, tanT, sinU, cosU and tanU. We'll be using trigonometric ratios to find their values.

‎

We know that,

‎

$\sf \Longrightarrow sin\theta = \dfrac{Side \ opposite \ to \ \theta}{Hypotenuse}$

‎

Let θ (the angle), be equal to ∠T.

‎

$\sf \Longrightarrow sinT = \dfrac{Side \ opposite \ to \ \angle T}{Hypotenuse}$

‎

$\sf \Longrightarrow sinT = \dfrac{SU}{TU}$

‎

SU = 12, and TU = 13, on substituting these values we get,

‎

$\sf \Longrightarrow \boxed{\textsf{\textbf{sinT}} = \dfrac{\textsf{\textbf{12}}}{\textsf{\textbf{13}}}}$

‎

Similarly, let θ (the angle) be equal to ∠U.

‎

$\sf \Longrightarrow sinU = \dfrac{Side \ opposite \ to \ \angle U}{Hypotenuse}$

‎

$\sf \Longrightarrow sinU = \dfrac{TS}{TU}$

‎

TS = 5, and TU = 13, on substituting these values we get,

‎

$\sf \Longrightarrow \boxed{\textsf{\textbf{sinU}} = \dfrac{\textsf{\textbf{5}}}{\textsf{\textbf{13}}}}$

‎

We also know that,

‎

$\sf \Longrightarrow cos\theta = \dfrac{Side \ adjacent \ to \ \theta}{Hypotenuse}$

‎

Let θ (the angle), be equal to ∠T.

‎

$\sf \Longrightarrow cosT = \dfrac{Side \ adjacent \ to \ \angle T}{Hypotenuse}$

‎‎

$\sf \Longrightarrow cosT = \dfrac{TS}{TU}$

‎‎

TS = 5, and TU = 13, on substituting these values we get,

‎‎

$\sf \Longrightarrow \boxed{\textsf{\textbf{cosT}} = \dfrac{\textsf{\textbf{5}}}{\textsf{\textbf{13}}}}$

‎

Similarly, let θ (the angle) be equal to ∠U.

‎

$\sf \Longrightarrow cosU = \dfrac{Side \ adjacent \ to \ \angle U}{Hypotenuse}$

‎

$\sf \Longrightarrow cosU = \dfrac{SU}{TU}$

‎

SU = 12, and TU = 13, on substituting these values we get,

‎

$\sf \Longrightarrow \boxed{\textsf{\textbf{cosU}} = \dfrac{\textsf{\textbf{12}}}{\textsf{\textbf{13}}}}$

‎

We also know that,

‎

$\sf \Longrightarrow tan\theta = \dfrac{Side \ opposite \ to \ \theta}{Side \ adjacent \ to \ \theta}$

‎

Let θ (the angle) be equal to ∠T.

‎

$\sf \Longrightarrow tan T = \dfrac{Side \ opposite \ to \ \angle T}{Side \ adjacent \ to \ \angle T}$

‎

$\sf \Longrightarrow tan T = \dfrac{SU}{TS}$

‎

SU = 12, and TS = 5, on substituting these values we get,

‎

$\sf \Longrightarrow \boxed{\textsf{\textbf{tanT}} = \dfrac{\textsf{\textbf{12}}}{\textsf{\textbf{5}}}}$

‎

Similarly, let θ (the angle) be equal to ∠U.

‎

$\sf \Longrightarrow tan U = \dfrac{Side \ opposite \ to \ \angle U}{Side \ adjacent \ to \ \angle U}$

‎

$\sf \Longrightarrow tan U = \dfrac{TS}{SU}$

‎

TS = 5, and SU = 12, on substituting these values we get,

‎

$\sf \Longrightarrow \boxed{\textsf{\textbf{tanU}} = \dfrac{\textsf{\textbf{5}}}{\textsf{\textbf{12}}}}$

‎‎

Hence solved.

Answer 2

$\boxed {\boxed{ { \green{ \bold{ \underline{Verified \: Answer \: }}}}}}$

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬

$\bigstar{\underline{\underline{{\sf\ \red{ SOLUTION:-}}}}}$

• REFER TO ATTACHMENT

▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬