唔識做功課69

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Let the height of the tree be h meters.
draw two right-angle triangles,
first with 30 degree, opposite side = (h - 1.9) meters, adj. side = x meters
second with 35 degree, opposite side = (h - 1.6) meters, adj. side = x meters

So, we have tan 30 = (h - 1.9) / x and tan 35 = (h - 1.6) / x
x = (h - 1.9) / tan 30 and x = (h - 1.6) / tan 35
(h - 1.9) / tan 30 = (h - 1.6) / tan 35
tan 35 (h - 1.9) = tan 30 (h - 1.6)
h tan 35 - 1.9 tan 35 = h tan 30 - 1.6 tan 30
h tan 35 - h tan 30 = 1.9 tan 35 - 1.6 tan 30
h(tan 35 - tan 30) = 1.9 tan 35 - 1.6 tan 30
h = (1.9 tan 35 - 1.6 tan 30) / (tan 35 - tan 30)
h = 3.31

therefore, the height of the tree is 3.31 meters