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# Need help setting up question....

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Question is:

During a windstorm, part of the top of a flagpole breaks off. The broken top portion touches the ground at an angle of 75 deg 19 feet from its base.

How tall was the pole before the windstorm?

I am having a hard time figuring out how exactly the sketch would be set up for me to start to solve the problem.

Guest Jan 10, 2016

#4
+78577
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The broken part will form the hypotenuse of a right triangle...call this x

And we know an angle and an adjacent side [19] to this angle.....

So.....the trig relationship  that best describes this is the cosine.....so

cos 75  = 19 / x     rearrange

x  = 19 / cos 75  = about 73.41 ft

And the height of the standing part, h, can be found by the tangent.....so we have

tan 75 = h / 19

h = 19 * tan 75 = about 70.91 ft

The total height of the pole is the sum of these =  73.41 + 70.91  = about 144.32 ft

CPhill  Jan 11, 2016
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#1
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During a windstorm, part of the top of a flagpole breaks off. The broken top portion touches the ground at an angle of 75 deg 19 feet from its base.

Tan(75)=Height of broken pole/19

3.732=H/19

H=19 X 3.732

H=70.908 feet-Length of the pole before windstorm.

Guest Jan 10, 2016
#2
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Solving for "a" only gives the broken flag pole length, so what would I do next to find the length of the broken portion?

Guest Jan 10, 2016
#3
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Because you have tow sides, use Pythagoras's Theorem:

Broken part=Hypotenuse

H^2=19^2 + 70.908^2

H^2=5,388.94 take the sqrt of both sides

H=73.41 feet-Length of the broken portion.

Guest Jan 10, 2016
#4
+78577
+10

The broken part will form the hypotenuse of a right triangle...call this x

And we know an angle and an adjacent side [19] to this angle.....

So.....the trig relationship  that best describes this is the cosine.....so

cos 75  = 19 / x     rearrange

x  = 19 / cos 75  = about 73.41 ft

And the height of the standing part, h, can be found by the tangent.....so we have

tan 75 = h / 19

h = 19 * tan 75 = about 70.91 ft

The total height of the pole is the sum of these =  73.41 + 70.91  = about 144.32 ft

CPhill  Jan 11, 2016

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