SOLUTION: if alpha and beta are acute angles with sin alpha=2/sqrt5 and beta=1/sqrt5, find exact value of sin(alpha+beta)

Question 84221: if alpha and beta are acute angles with sin alpha=2/sqrt5 and beta=1/sqrt5, find exact value of sin(alpha+beta)
Answer by tutor_paul(519) (Show Source): You can put this solution on YOUR website!
The equation to use is:

You are given and , so you need to get and before you can solve the problem.
You can apply the Pythagorean theorem to see that the adjacent side of the triangle (x) to alpha = 1; Similarly, apply the Pythagorean theorem to see that the adjacent side of the triangle (y) to beta = 2:

and:

===========================
Now you can figure out that

and

===========================
Now just plug and chug in the original equation:

Good Luck,
tutor_paul@yahoo.com
RELATED QUESTIONS
cos alpha= 1/2and tan beta=1/3.find sin(alpha+beta),where alpha and beta are both acute... (answered by Theo,harpazo)

Please help me solve this question If alpha and beta are 2 positive acute angles... (answered by ikleyn)

Find the exact value for sin(alpha-beta) if sin(alpha) = -5/13 and cos(beta) = -8/17 with (answered by ikleyn)

if sin(alpha) = 0.954 and sin(beta) = 0.306 with both angles' terminal rays in quadrant... (answered by ikleyn)

If alpha and beta are acute angles such that csc alpha = 17/15 and cot beta = 5/12, find... (answered by ewatrrr)

Find the exact value for cos(alpha+beta) if sin(alpha) = -3/5 and sin(beta) = 5/13 with... (answered by Fombitz,MathTherapy,ikleyn)

Find the Exact value (No Decimals) of sin(105 degrees) using the sum or difference... (answered by Theo)

Given that sin(alpha)=2/3 and sin(beta)=-1/3 with alpha in Quadrant 2 and beta in... (answered by lwsshak3)

If alpha+beta=90� and sin(alpha)=1/3,then Sin(beta) is ? (answered by ikleyn)