Question 901286
you have cosine(a) = 1/2
this means that adjacent side is 1 and hypotenuse is 2.
use pythagorus to find that opposite side is sqrt(3)


you have tan(b) = 1/3
this means that opposite side is 1 and adjacent side is 3.
use pythagorus to find that hypotenuse is sqrt(10)


pythagorus is a^2 + b^2 = c^2 where c is the hypotenuse and a and b are legs.


sin(a+b) = sin(a) * cos(b) + cos(a) * sin(b)


sin(a) = sqrt(3)/2
cos(b) = 3/sqrt(10)
cos(a) = 1/sqrt(10)
sin(b) = 1/2


formula becomes:


sin(a+b) = sqrt(3)/2 * 3/sqrt(10) + 1/sqrt(10) * 1/2


cimplify that to get:


(sqrt(3)*3)/(2*sqrt(10) + (1*1)/(2*sqrt(10)


combine into one common denominator and you get:


(3*sqrt(3) + (1*1) / (2*sqrt(10)


use your calculator to solve to get sin(a+b) = .9796927193


take the arcsine of that to get (a+b) = 78.43494882 degrees.



a = 60 degrees.
b = 18.43494882 
a+b = 78.43494882 degrees.


you were asked to find sin(a+b), so your solution is:


sin(a+b) = .9796927193