In trisngle RST, angle S is a right angle and csc R=5/3. T=What is tan T?

sin R = 3/5 = r/s

t^2 = 5^2 - 3^2 = 25 - 9 = 16
so t = 4

tan T = t/s = 4/5

Your answer is wrong. You forgot to switch csc into sin, therefore r=3, and s=5. Now we know that tan (T)= 4/3

To find the value of tan(T) in triangle RST, we need to know the values of angle T and the length of side TS. However, the given information only includes the fact that angle S is a right angle and csc(R) = 5/3.

To solve this problem, we need to determine the value of angle R. The cosecant (csc) of an angle is equal to the reciprocal of the sine (sin) of that angle. Therefore, csc(R) = 5/3 is equivalent to sin(R) = 3/5.

In a right triangle, the sine (sin) of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In triangle RST, the side opposite angle R is side ST (the hypotenuse is the longest side and not involved in calculating the tangent), so sin(R) = ST/TS.

From the previous information, we know that sin(R) = 3/5, which means ST/TS = 3/5. We can then use this information to find the value of tan(T).

The tangent (tan) of an angle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle. In this case, the side opposite angle T is ST, and the side adjacent to angle T is RS.

Since ST/TS = 3/5, we can set up the equation:

ST/RS = 3/5

To isolate ST, we can multiply both sides of the equation by RS:

ST = (3/5) * RS

Now we have the value of ST, we can determine the value of tan(T):

tan(T) = ST/RS = (3/5) * RS / RS = 3/5

Therefore, the value of tan(T) in triangle RST is equal to 3/5.