sinA=根5/5 ,sinB=根10/10 ,0小于A小于90 ,0小于B小于90,则A+B=

题目

sinA=根5/5 ,sinB=根10/10 ,0小于A小于90 ,0小于B小于90,则A+B=

答案

∵a、b是锐角,
sina=√5 / 5
cosa=√（1-sin²a）=2√5/5.
sinb=√10/10,
cosb=√(1-sin²b)=3√10/10
sin(a+b)=sina cosb + cosa sinb
=√2/2
→ a+b =45° 或 a+b =135°
∵sina=√5/5 < 0.5
sinb=√10/10
∴0°< a