Question

An acute angle θ is in a right triangle with sin θ = five sixths. what is the value of cot θ? five divided by the square root of eleven six divided by the square root of eleven square root of eleven divided by five square root of eleven divided by six

Answer 1

The value of cot θ in a right triangle with sin θ = 5/6 is √11 / 5.

Step-by-step explanation:

The student asked for the value of cot θ in a right triangle where sin θ = 5/6. Since we know that cot θ = 1/tan θ and that tan θ = sin θ/cos θ, we can find cot θ by using the Pythagorean theorem to find cos θ first. Given sin θ = 5/6, we can say that opposite side (y) = 5 and hypotenuse (h) = 6. We then use Pythagorean theorem to find the adjacent side (x): x = √(h² - y²) = √(6² - 5²) = √(36 - 25) = √11. Finally, cos θ = x/h = √11/6, and cot θ = 1/tan θ = cos θ/sin θ = (√11/6) / (5/6) = √11 / 5.