if sinp =3/5 and p is an acute angle find tanP
You should recognize the 3-4-5 right-angled triangle, so
cosp = 4/5
tan p = sinp/cosp = (3/5) / (4/5) = 3/4
draw a right triangle with sinP=3/5
That is, opposite/hypotenuse = 3/5
Now surely you recognize a 3-4-5 right triangle, so the adjacent side is 4.
Or, if you want to do the math, it is √(5^2-3^2) = 4
tanP = opposite/adjacent = 3/4
To find the value of tan(P), where sin(P) = 3/5 and P is an acute angle, we can use the relationship between sine, cosine, and tangent.
We know that sin(P) = 3/5, which means the opposite side of the right triangle formed by angle P is 3 and the hypotenuse is 5. Let's call the adjacent side x and the opposite side 3.
Using the Pythagorean theorem, we can find the value of x:
(x^2) + (3^2) = (5^2)
x^2 + 9 = 25
x^2 = 25 - 9
x^2 = 16
x = √16
x = 4
So, the adjacent side of the right triangle is 4.
Now, we can use the definition of tangent to find tan(P):
tan(P) = opposite/adjacent
tan(P) = 3/4
Therefore, tan(P) = 3/4.