Question

An acute angle θ is in a right triangle with sin θ = 5/6 . What is the value of cot θ?

Answer 1

Answer:
`(√(11))/(5)`

Explanation:

sin =
`(opposite)/(hypotenuse)`

It is given that sin θ =
`(5)/(6)`. Use the Pythagorean Theorem to find the length of the adjacent side:

a² + b² = c²

5² + b² = 6²

25 + b² = 36

b² = 11

`\sqrt{b^(2)} = √(11)`

b =
`√(11)`

adjacent =
`√(11)`, opposite = 5, hypotenuse = 6

cot =
`(adjacent)/(opposite)`

=
`(√(11))/(5)`