Question

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! Please help! Thanks!

Answer 1

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

Answer 2

Here's a better look at the answer

\[\Large \cot(\theta) = \frac{\sqrt{5}}{2}\]

Answer 3

Huh! So I did do it right! I must have done the math wrong! Thanks for the clarification! :)

Answer 4

yw