![](https://video.ask-data.xyz/img.php?b=https://iknow-pic.cdn.bcebos.com/b7003af33a87e950f3d253dd13385343faf2b4be?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_600%2Ch_800%2Climit_1%2Fquality%2Cq_85%2Fformat%2Cf_auto)
解:连结AD,在△ACD中,由余弦定理可得
AD
2=AC
2+CD
2-2AC?CDcos91.2°
=3.7
2+5.2
2-2×3.7×5.3×(-0.0209)
=41.5,
∴AD=6.4(km).在△ADC中,由正弦定理可得
sin∠CDA=
=0.1562.
∴∠CDA=9°,
在△ADB中,由余弦定理可得
AB
2=AD
2+BD
2-2AD?BDcos(113.4°-9°)=6.4
2+2.9
2-2×6.4×2.9×(-0.2486)
=427.29.
解得AB=20.7km.
所以A、B之间的距离为:20.7km.