如圖為測量山高MN，以A點及另一座山的山頂C為觀測點，從A點測得M點的仰角∠MAN=60∘，C點的仰角∠CAB=45∘以及∠MAC=75∘，從C點測得∠MCA=60∘，已知山高BC¯=100m，則山高MN?

令 MN = h
AM = h * csc ∠MAN = h * csc 60° = h * ( 2 / √3 ) = ( 2√3 / 3 ) h
AC = BC * csc ∠CAB = 100 * csc 45° = 100√2
∠AMC = 180° - ∠MAC - ∠MCA = 180° - 75° - 60° = 45°

在 ΔACM 中, 由正弦定理得 :
AM / sin ∠MCA = AC / sin ∠AMC
AM / sin 60° = AC / sin 45°
AM * sin 45° = AC * sin 60°
( 2√3 / 3 ) h * ( √2 / 2 ) = 100√2 * ( √3 / 2 )
( √6 / 3 ) h = 50√6
h = 150

Ans: 150 m