Question

If sin theta = 15/17, use pythagoren theorem to identify to find cos theta?

Answer 1

cosθ =
`(8)/(17)`

Explanation:

given

sinθ =
`(15)/(17)` =
`(opposite)/(hypotenuse)`

this is a right triangle with legs opposite (o) and adjacent (a) and hypotenuse (h)

using Pythagoras' identity in the right triangle

h² = a² + o² , that is

17² = a² + 15²

289 = a² + 225 ( subtract 225 from both sides )

64 = a² ( take square root of both sides )

`√(64)` = a , so

adjacent a = 8

then

cosθ =
`(adjacent)/(hypotenuse)` =
`(8)/(17)`