Question

if cos=3/5, then tan=

Answer 1

This is a 3-4-5 triangle.

Remember, 
SOH-CAH-TOA

S(ine) =  O(pposite)/H(ypotenuse)
C(osine) = A(djacent)/H(ypotenuse)
T(angent) = O(pposite)/A(djacent)

In Cosine, the adjacent = 3, and the Hypotenuse = 5

Hypotenuse is the longest side. 

3,4,5 is the triangle that fits inside, therefore, the Opposite is 4, and Adjacent is 3

T(angent) = O(pposite)/A(djacent)

Plug in the numbers

T = 4/3

tan = 4/3 is your answer

hope this helps

Answer 2

So cosФ = 3/5 means that ratio of length of adjacent side to length of hypotenuse side is 3:5

So then we can assume adjacent side is 3 and hypotenuse is 5.

By Pythagoras' Theorem, we have √(5² - 3²) = 4, so then length of opposite side would be 4.

Now tanФ is ratio of length of opposite side to length of adjacent side, which would be 4/3.

Final answer: 4/3

Hope this helps.