If sin A=1/3 find cos A ( A= acute angle
Answers
Step-by-step explanation:
Given :-
Sin A = 1/3
A is an acute angle.
To find :-
Find the value of Cos A ?
Solution :-
Method -1:-
Given that
Sin A = 1/3
On squaring both sides then
=> (Sin A)² = (1/3)²
=> Sin² A = 1/9
On subtracting the above equation from 1 then
=> 1-Sin² A = 1-(1/9)
=> Cos² A = (9-1)/9
Since , Sin² A + Cos² A = 1
=> Cos² A = 8/9
=> Cos A = √(8/9)
=> Cos A = √8/3
=> Cos A = (2√2)/3
Therefore, Cos A =√8/3 or (2√2)/3
Method -2:-
Given that
Sin A = 1/3
Consider a right angled triangle ABC,
Sin A = 1/3
=> Opposite side to < A / Hypotenuse = 1/3
=> BC/AC = 1/3
Let BC = 1k
Let AC = 3k
By Pythagoras Theorem,
AC² = AB²+BC²
=> (3k)² = AB²+(1k)²
=> 9k² = AB² + k²
=> AB² = 9k²-k²
=> AB² = 8k²
=> AB = √(8k²)
=> AB = √8 k
Now,
CosA = Adjacent side to <A/ Hypotenuse
=> Cos A = AB/AC
=> Cos A = √8 k/3k
=> Cos A = √8/3
or
=> Cos A =( 2√2 )/ 3
Answer:-
The value of Cos A for the given problem is √8/3 or (2√2)/3
Used formulae:-
→ Sin A = Opposite side to < A / Hypotenuse
→ CosA = Adjacent side to <A/ Hypotenuse
→ Sin² A + Cos² A = 1
Pythagoras Theorem:-
" In a right angled triangle The square of the hypotenuse is equal to the sum of the squares of the other two sides".
Answer:
the answer is 2√2/3 , I hope you are happy to see this answer