If Cos A = 2/3 then find the value of Sin A and Tan A.
Answers
Answer:
cos A=2/3
Step-by-step explanation:
(hyp)^=s^+s^
3^=s^+2^
9=s^+4
9-4=s^
5=s^
√5=s
sinA=opposite/hypotenuse=√5/3
tanA=opposite/adjacent=√5/2
sinA= √5/3 and tanA= √5/2
Given:
cosA = 2/3
To Find:
Value of sinA and tanA
Solution:
We know that for a right-angled triangle
cosA= Base/ Hypotenuse _(1)
given, cosA= 2/3 _(2)
Comparing _(1) and (2)
Base= 2 and Hypotenuse= 3
Using Pythagoras Theorem
(Hypotenuse)²= (Base)²+ (Perpendicular)²
(3)²= (2)²+ P²
9= 4+ P²
P²= 9-4
P= √5
Using ratio formulas of sinA and tanA
sinA= Perpendicular/ Hypotenuse
Putting values of perpendicular and hypotenuse in the above formula
sinA= √5/3
Also tanA= Perpendicular/Base
tanA= √5/2
Hence, the value of sinA is √5/3, and the value of tanA is √5/2.
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