如图,在△ABC中,角C=90°,角A=15°.求:(1)AC:BC的值 (2)求sinA的值

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如图,在△ABC中,角C=90°,角A=15°.求:(1)AC:BC的值 (2)求sinA的值

如图,在△ABC中,角C=90°,角A=15°.求:(1)AC:BC的值 (2)求sinA的值
如图,在△ABC中,角C=90°,角A=15°.求:(1)AC:BC的值 (2)求sinA的值

如图,在△ABC中,角C=90°,角A=15°.求:(1)AC:BC的值 (2)求sinA的值
tan15° = sin15° /cos15°
= √¯[(1 - cos30° )/(1 + cos30° )]
= √¯[(2 - √¯3)/(2 + √¯3)]
= (2 - √¯3)
注:AC:BC=1:2 - √¯3
sin15° = √¯[(1 - cos30° )/2]

tan15° = sin15° /cos15°
= √¯[(1 - cos30° )/(1 + cos30° )]
= √¯[(2 - √¯3)/(2 + √¯3)]
= (2 - √¯3)
注:AC:BC=1:2 - √¯3
sin15° = √¯[(1 - cos30° )/2]

AC:BC=cot∠A=cot15°=cot(45°-30°)=(cot45°cot30°+1)/(cot30°-cot45°)=(√3+1)/(√3-1)=(√3+1)²/2=2+√3
sinA=sin15°=sin(45°-30°)=sin45°cos30°-cos45²sin30°=√2/2*√3/2-√2/2*1/2=(√6-√2)/4