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The CN Tower in Toronto is the second-tallest free-standing structure in the world, at a height of 555 metres (more than half a kilometre!) Buddy is standing due west of the tower, and Holly is standing due east of it. Buddy and Holly talk to each other on cell phones. Buddy says that the top of the CN Tower is elevated 40º from the horizon from where he is standing. Holly says that the top is 10º from where she is standing. How far apart are Buddy and Holly from each other?

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budwilkins
Make a large triangle with the apex the tower and the two lower vertices each where Buddy and Holly stand. They each have their own right triangle inside of the large one. The tower forms 90 degrees with the ground.
Triangles have 180 degrees, so Buddy's triangle has an apex of 180-90-40 = 50
Holly's apex is 180-90-10 = 80
The tower's height = 555m
So tangent of 40 = 555/x
Therefore Buddy's base (x) = 555/tan40
x = 661.4 m
Holly's distance from the tower = y
tangent of her angle (10) = 555/y
y = 555/tan10 = 3147.6 m
their distance apart = x + y
x + y = 661.4 + 3147.6 = 3809 m

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