Question

In A ABC, right-angled at B, AB = 24 cm. BC=7 cm. Determine: (1) sin A, COS A (ii) sin C, cos C​

Answer 1

Answer:

R.E.F image

In Δ ABC, B is at right angle.

Given, AB=24cm

BC=7cm

using Pythagoras theorem  

AB  

2

+BC  

2

=AC  

2

 

⇒(24)  

2

+(7)  

2

=AC  

2

 

⇒AC=  

(24  

2

)+(7)  

2

 

​

=  

576+49

​

=  

625

​

 

⇒AC=25CM

(i)sin A=  

AC

BC

​

 

=  

25

7

​

 

cos A=  

AC

AB

​

 

=  

25

24

​

 

(ii)sin C=  

AC

AB

​

 

=  

25

24

​

 

cos c=  

AC

BC

​

 

=  

25

7

​

   

Step-by-step explanation:

Answer 2

$\footnotesize \text \blue{➝ Given:-}$

$\:$

$\footnotesize \text{➝ Right-angled at B}$

$\footnotesize \text{➝ AB = 24 cm}$

$\footnotesize \text{➝ BC = 7 cm}$

$\:$

$\footnotesize \text \blue{➝ Solution:-}$

$\:$

$\footnotesize \text \blue{➝ First find AC (By Pythagoras Theorem)}$

$\:$

$\footnotesize \text{➝ (AC)² = (AB)² + (BC)²}$

$\footnotesize \text{➝ (AC)² = (24)² + (7)²}$

$\footnotesize \text{➝ (AC)² = 576 + 49}$

$\footnotesize \text{➝ (AC)² = 625}$

$\footnotesize \text{➝ AC = √625}$

$\underline{ \underline{ \boxed{ \footnotesize \text \blue{➝ AC = 25}}}}$

$\:$

$\footnotesize \text{➝ </p><p>Sin A = BC / AC }$

$\underline{ \underline{ \boxed{ \footnotesize \text \blue{➝ Sin A = 7/25}}}}$

$\:$

$\footnotesize \text{➝ </p><p>Cos A = AB / AC }$

$\underline{ \underline{ \boxed{ \footnotesize \text \blue{➝ Cos A = 24/ 25}}}}$

$\:$

$\footnotesize \text{➝ </p><p>Sin C = AB / AC }$

$\underline{ \underline{ \boxed{ \footnotesize \text \blue{➝ Sin C = 24/25}}}}$

$\:$

$\footnotesize \text{➝ </p><p>Cos C = BC / AC }$

$\underline{ \underline{ \boxed{ \footnotesize \text \blue{➝ Cos C = 7/25}}}}$

$\:$

Note:- The side in front of theta is always considered as Perpendicular (P)