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Question

Two spruce trees are 100m apart. From the point on the ground halfway between the trees the angles of elevation are 21 degrees and 39 degrees. Determine the distance, to the nearest metre, between the tops of the two trees. Show your work.

Answer 1

find the heights of the two trees
... 50m tan(21º) and 50m tan(39º)

the difference in the heights is the vertical distance between the tops

the horizontal distance is 100m

(total distance)^2 = (vertical distance)^2 + (horizontal distance)^2

Answer 2

make your sketch , to get 2 right-angled triangles, both with a base of 50
From midpoint of base,
distance to top of taller tree ---- x
distance to top of smaller tree --- y
cos39 = 50/x ----> x = 50/cos39
cos21 = 50/y ---> y = 50/cos21

D^2 = x^2 + y^2 - 2xy cos120
D = ...