Question

if sin a = √5/5 and sin b = √10/10,where a and b are acute find
Cos A

Answer 1

is the problem:
if \(\sin(\alpha)=\frac{\sqrt{5}}{5}\) find \(\cos(\alpha)\) ?

Answer 2

Yes

Answer 3

can u write the exact question

Answer 4

use cosA=sqrt(1-(sina)^2)=sqrt(1-5/25)=sqrt(4/5) =2/sqrt(5)

Answer 5

there is a picture of an angle whose sine is \(\frac{\sqrt{5}}{5}\) what you need is the adjacent side, which you can find by pythagoras
\[\sqrt{5}^2+a^2=5^5\]
\[5+a^2=25\]
\[a^2=20\]
\[a=\sqrt{20}=2\sqrt{5}\]

Answer 6

the the ratio for cosine would be
\[\cos(\alpha)=\frac{2\sqrt{5}}{5}\]