Question

HELP!!! 15 points. picture below

Answer 1

Explanation:

`\sin( \alpha ) = ( √(5) )/(3) \\ \alpha = 48.19 \: degrees \\ \cos( \alpha ) = (2)/(3)`

Answer 2

cos theta =± 2/3

Explanation:

sin theta = sqrt(5) /3

sin theta = opp side / hypotenuse

We know that

a^2 + b^2 = c^2 from the pythagorean theorem

opposite side ^2 + adjacent side ^2 = hypotenuse ^2

( sqrt(5)) ^2 + adjacent side ^2 = 3^2

5 + adjacent side ^2 = 9

Subtract 5 from each side

5-5 + adjacent side ^2 = 9-5

adjacent side ^2 = 4

Taking the square root of each side

adjacent side = ±2

We know that

cos theta = adj side / hyp

cos theta =± 2/3