Question

Express your answer exactly

Answer 1

sin(θ) =
`(√(55) )/(8)`

Explanation:

See the attachment.

Cosine is adjacent over hypotenuse, so since cos(θ) = 3/8, then the adjacent side of the triangle is 3 and the hypotenuse is 8.

Since is opposite divided by hypotenuse. To find the opposite side, which is the unlabelled side on the graph, we need to use the Pythagorean Theorem:

x =
`√(8^2-3^2) =√(64-9) =√(55)`

So, sin(θ) =
`(√(55) )/(8)`.

Hope this helps!