another question ?
A is an acute angle and sin A=3/5 calculate the value of tan A ??
did your teacher specify if you need an exact number or a fraction will do just fine??
Well, I guess it doesn't really matter. Ok it helps if you draw your triangle, but you don't necessarlly have to. You know that A must be less than 90 and that its sin= 3/5. sin= opposite side of the angle/ the hypot. If you drew a triangle you'll notice that its a 3,4,5 triangle. Your tan = 3/4.
To calculate the value of tan A, we can use the relationship between sine (sin) and tangent (tan).
The relationship is as follows:
tan A = sin A / cos A
Since we are given sin A = 3/5, we need to find cos A in order to calculate tan A.
To find cos A, we can use the relationship between sine, cosine, and the Pythagorean identity:
sin^2 A + cos^2 A = 1
Rearranging the equation, we get:
cos^2 A = 1 - sin^2 A
Plugging in the value of sin A = 3/5, we get:
cos^2 A = 1 - (3/5)^2
= 1 - 9/25
= 16/25
Taking the square root of both sides, we get:
cos A = ± (4/5)
Since A is an acute angle, the value of cos A is positive. Therefore:
cos A = 4/5
Now that we have both sin A and cos A, we can substitute them into our original equation to calculate tan A:
tan A = sin A / cos A
= (3/5) / (4/5)
= 3/4
So the value of tan A is 3/4.