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第 19 週 · 三角學(二)立體 · 第 5 節

立體應用題(四步拆解法)

立體題看著嚇人,但有固定四步就能拆 — 畫立體圖、找含未知量的直角三角形、把它單獨重畫、再用勾股或三角比求解。長方體、角錐、棱柱通通照辦。配滿立體圖例。

▶ 第一關: 四步拆解法
1draw the 3D solidlabel all known edges / heights2find the right trianglethe one holding the unknown3redraw it ALONE (key step)flat 2D → see the hypotenuse4solve: Pythagoras / trigtwo sides → side; angle → sin cos tan
3D figure (find it)pull it out, flatlegleghyp
▶ 第二關: 長方體應用
base diag 15space diag = 17h 8129
step A: base triangle12915step B: vertical triangle15817
▶ 第三關: 角錐(金字塔)應用
apexheighthalf-baseslant
slant triangle pulled outhalf-base 3h 4slant 5
lateral face = isosceles trianglehalf-base 3slant 4edge 5
dihedral angle (face vs base)θ=45half-base 5h 5
⚔ BOSS: 立體綜合多步
ant path= 17base diag 151298