# math

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a pole leans away from the sun at an angle of 7 degrees to the vertical. when the elivation of the sun is 48 degrees the pole cast a shadow of 41ft long on level ground. how long is the pole?

• math -

a is vertically under pole, base to tip
41 - a is shadow tip from under pole tip

height of pole = y cos 7 = .993 y
tan 48 = .993 y/(41-a)

tan 7 = a/y so a = y tan 7

then
tan 48 = .993 y/(41 -y tan 7) solve for y

• math -

Draw a big diagram

You end up with a triangle with:

the horizontal side = 47 ft

the side representing the leaning pole ... call it a

and the angle opposite the pole side = 51°

The pole makes an angle of 7° with the vertical ... so the angle between to pole side and the 47ft side = 90 - 7 = 83°

So that make the angle opposite the 47 ft side = 180 - (51 + 83) = 46°

Now you can use the sine rule to find the length of the pole:

a/sin51° = 47/sin46

a = 47 * sin51 / sin46

a = 50.8 ft

so the length of the pole is 50.8 ft

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