A fence post is 47.0m from where you are standing, in a direction 40.0 degrees north of east. A second fence post is due south from you. What is the distance of the second post from you, if the distance between the two posts is 70.0m ?
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North distance component of post 1 from you = (sin 40) x 47, = 30.21m.
East component = (cos 40) x 47, = 36m.
From that, you can "construct" a long right triangle, the base of which is 36m., with a hypotenuse of 70m.
The 3rd. side length (North/ South distance between posts) will be sqrt. (70^2 - 36^2) = 60.03 metres.
(60.03 - 30.21) = 2nd. post 29.82 metres south of you.
East component = (cos 40) x 47, = 36m.
From that, you can "construct" a long right triangle, the base of which is 36m., with a hypotenuse of 70m.
The 3rd. side length (North/ South distance between posts) will be sqrt. (70^2 - 36^2) = 60.03 metres.
(60.03 - 30.21) = 2nd. post 29.82 metres south of you.