If sin p =2/8 and p is an acute angle, what is the value of tan p?

Answer 1

sin p =2/8 = 1/4
I constructed a right-angled triangle with r = 4, y = 1 and p the base angle
x^2 + y^2 = r^2
x^2 + 1 = 16
x^2 = 15
x = ± √15

tan p = y/x
tan p = 1/√15 or tan p = -1/√15 , since you did not specify the domain of p

Answer 2

since p is an acute angle, just draw a right triangle with
opposite leg = 2
hypotenuse = 8
the adjacent leg is thus √60
so tan p = 2/√60 = 1/√15