An acute angle θ is in a right triangle with sin θ =2/3 . what is the value of cot θ?
i found that 2 is the opposite angle and 3 is the hypotenuse.
adj/opp = cot θ, so adj/2 = cot θ
i tried using the pythagorean theorem, but i can get an answer choice! ! !

The adjacent side can be found by the Pythagorean Theorem
a^2 + b^2 = c^2
x^2 + 2^2 = 3^2
x^2 + 4 = 9
x^2 = 9-4
x^2 = 5
x = sqrt(5)
So the adjacent side is sqrt(5) units
which means
cot(theta) = adj/opp
cot(theta) = sqrt(5)/2

The value of cot θ is:

           

Step-by-step explanation:

We are given:

     

We know that the sine trignometric function is the ratio of the perpendicular to hypotenuse of the triangle corresponding to θ.

i.e. Perpendicular=2 units

and Hypotenuse = 3 units

We know that in a right angled triangle with leg lengths as a, b and hypotenuse c the Pythagorean Theorem says that:

This means we get Base=√5 units

Also, we know that:

 

                       Hence, we get:

           

= 10n - 111

Step-by-step explanation:

The first term of the sequence is - 101

we need to confirm that the sequence is arithmetic , that is , if it is arithmetic , it must have a common difference (d).

d = second term - first term = third term - second term

d = -91 - (-101)

d = -91 + 101

d = 10

Therefore the formula for the nth term is given as:

= a + (n - 1 ) d

= - 101 + (n - 1) 10

= - 101 + 10n - 10

= -111 + 10n

Therefore :

= 10n - 111