Question

8 points! Please help me with this problem, what is sin(theta)?

Answer 1

`(√(17) )/(7)`

Explanation:

Given

cosΘ =
`(4√(2) )/(7)` =
`(adjacent)/(hypotenuse)`

Then the hypotenuse of the right triangle is 7 and the adjacent side is 4
`√(2)`

To find the opposite side use Pythagoras' identity

The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is

opp² + (4
`√(2)` )² = 7²

opp² + 32 = 49 ( subtract 32 from both sides )

opp² = 17 ( take the square root of both sides )

opp =
`√(17)`

Hence

sinΘ =
`(opposite)/(hypotenuse)` =
`(√(17) )/(7)`

Answer 2

sin=√17/7

or sin=sqrt(17)/7