Finding a missing distance/angle

J

jcasqueiro

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May 2, 2019
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Hi,
Can anyone help me find the solution to the problem attached algebraically? I need to find distance D and angle a (figure not at scale).
Thanks/Brgds
11975
 
Last edited:
What tools have you?

Sum or EXterior angles of a closed polygon?
Draw some interior lines or extensions to cut things down to triangles?

Demonstrate your work, please.
 
One way is to draw in the diagonal through the 40 degree angle and solve the triangle to its right, finding the length of the diagonal and the angles. Then you can solve the triangle on the left to find what you need.

I assume you know the laws of sines and cosines?
 
Hmmm...I suggest you get a sheet of graph paper
and plot your polygon AT LEAST close to scale.
As shown, it is ridiculously misleading...
That 40 degrees angle is inside the polygon?
 
The problem isn't really affected by the not-to-scale drawing, fortunately. Here's an accurate one:
FMH115827.png
 
Hmmm, thanks DrP...we can draw perpendicular BE to AD, then solve triangle ABE.
Probably not the ideal "1st step"...
 
Thanks for all your inputs. Dr.P picture is quite enlightning.
Geometrically it's easy to find the answer, I was a little lost on how to deal with it algebraically.
 
My solution is trigonometric (neither purely geometric nor purely algebraic). Are you saying you solved it without trig? Or did you do the trig without any algebraic formulations? I'd like to see your method.

My method, as I hinted, is to use the Law of Cosines on the first triangle, then the Law of Sines on the second.
 
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