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angle between line and plane

發問:

圖片參考：http://imgcld.yimg.com/8/n/HA00510450/o/701104170095913873427860.jpg find the angle between the line VG and the plane ABC. Hence,find the inclination of the line of greatest slope of the plane VAB

最佳解答:

CA=CB VA=VB=10 cm △CAB and △VAB are isos. triangles. G is the mid-point of AB. VG is perpendicular to AB. ∴ ∠VGC is the angle between the line VG and the plane ABC. The line VG is the line of greatest slope. In rt∠△AGC, ∠ACG=50?/2=25? cos∠ACG=CG/AC cos25?=CG/8cm CG=7.2505 cm In rt∠△VCG, tan∠VGC=VC/CG=6/7.2505=0.8275 ∠VGC=39.6087? ∴ The angle between the line VG and the plane ABC is 39.61? (corr. to 2 d.p.) The inclination of the line of greatest slope is 0.83 (corr. to 2 d.p.)

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