Given that sin a = 3/5 and a is in the interval (90,180), calculate tan a.

If the angle a is in the interval (90,180), that means
that the angle is located in the 2nd quadrant, then the value of tangent function is
negative.

The tangent function is the
ratio:

tan a = sin a/ cos
a

Since the value of cos a is negative in the second
quadrant, that means that the value of the ratio is negative,
too.

We'll calculate cos a from the fundamental formula of
trigonometry:

(sin a)^2 + (cos a)^2 =
1

9/25 + (cos a)^2 = 1

We'll
subtract 9/25 both sides:

(cos a)^2 = 1 -
9/25

(cos a)^2 =
(25-9)/25

(cos a)^2 =
16/25

cos a = -4/5

We'll
choose only the negative value for cos a, since a is in the 2nd
quadrant.

tan a =
-(3/5)*(5/4)

 We'll reduce the like
terms:

tan a =
-3/4