Find the exact length of the third side

If a and b are the measures of two first quadrant angles and sin a = 4/9 and sin b = 2/5 find sin(a+b).

Can someone check if i did this correct. it’s number 4 if you’re wondering.

Recall that the owner of a local health food store recently started a new ad campaign to attract more business and wants to know if average daily sales have increased. historically average daily sales were approximately $2,700. the upper bound of the 95% range of likely sample means for this one-sided test is approximately $2,843.44. if the owner took a random sample of forty-five days and found that daily average sales were now $2,984, what can she conclude at the 95% confidence level?