5sin²a+4cos²a=9/2 find tan a
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5(sin²a)+ 4cos²a=9/2
5sin²a+4(1-sin²a)= 9/2
5sin²a+4-4sin²a=9/2
sin²a=9/2-4
sin²a=1/2
sina= 1/√2
by Pythagoras therom
ac²=bc²+ab²
(√2)²=bc²+(1)²
bc= 1
tana =ab/bc
tana=1
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