Question

An acute angle theta is in a right triangle with sin theta 3/4. What is the value of cot theta

Answer 1

cotΘ=(3√7)/7 i hope this helped you

Answer 2

cot θ =
`√(7) /3`

Explanation:

sin θ = opposite side / hypotenuse

Therefore, in this triangle:

opposite side = 3 and hypotenuse = 4

To find the other cathet we are going to use the Pythagorean Theorem:

`cathet^(2)= 4^(2) -3^(2) \\cathet^(2) =16-9\\cathet^(2) =7\\cathet=√(7)`

So the adjacent side is
`√(7)`

Now, we know that cot θ = adjacent side / opposite side. Therefore:

cot θ =
`√(7) /3`