SOLUTION: Please help me to solve this equation. If sin p=3/5 and p is an acute angle, what is the value of tan p ?

Since 'p' is an acute angle, it is in first quarter.


So, we can think about a right-angled triangle, in which 'p' is one angle 
and '3' is the opposite leg, while '5' is the hypotenuse.


Then the adjacent leg is   =  =  = 4.


Hence,  tan(p) is the ratio   = .


At this point, the solution is complete,

and the  ANSWER  is  tan(p) = .

You must be beginning trig, so I'll go a little easier.



We can use the numerator 3 for "a", and the denominator 5 for "c".

Sketch a right triangle with angle "p", side opposite angle "p" as "a",
hypotenuse as "c", and side adjacent to angle "p" as "b". 





The only side that is unknown is the adjacent side to angle "p", which is "b".

So we use the Pythagorean theorem, which is

 

and substitute a=3 and c=5








Now we have side adjacent to angle "p", b=4
 


Now we can find tan(p):





Edwin