Question

An acute angle θ is in a right triangle with sin θ = eight ninths. What is the value of cot θ?

Answer 1

I hope this helps you

Answer 2

`cot\theta =(√(17))/(8)`

Explanation:

We have

`sin\theta =(8)/(9)`

We know that

`cot\theta =(cos\theta)/(sin\theta)`

`cos\theta =√(1-sin^2\theta)=\sqrt{1-\left ((8)/(9) \right )^2}=\sqrt{1-(64)/(81)}=(√(17))/(9)`

Substituting

`cot\theta =((√(17))/(9))/((8)/(9))=(√(17))/(8)`