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February 1st, 2010, 04:27 AM   #1
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Length of sides and angle calculations

Hi,

Can someone tell me how I would find a) the length of side BC and

b) the angle B,on the sketch,


Thanks....[attachment=0:3nsc7msn]01-02-2010 12-45-26_0063.jpg[/attachment:3nsc7msn]
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February 1st, 2010, 11:38 AM   #2
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Is AC perpendicular to BD? You need some extra piece of information such as that.
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February 1st, 2010, 01:18 PM   #3
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Re: Length of sides and angle calculations

Hello, manich44!

I explained this at another site.

We are given three sides and one angle of a quadrilateral.
[color=beige]. . [/color]This does not determine a unique quadrilateral.


We find that:[color=beige] .[/color]

Then we have , but we know only two of its sides.


If , we have a chance . . .


~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Hello, skipjack!

I thought of that, too.

But if , we'd have a kite and

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February 2nd, 2010, 01:23 AM   #4
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Re: Length of sides and angle calculations

Sorry Guys,

Forgot to include total area = 1276m2
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February 2nd, 2010, 07:19 AM   #5
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Area triangle ADB = (1/2)(34.37)(41.45)sin(105.24)m = 687.26831m
Area triangle CDB = 1276m - 687.26831m = 588.73169m
By the cosine rule, BD = (34.37 + 41.45 - 2(34.37)(41.45)cos(105.24))m = 3648.3673m,
so BD = 60.4017164m

Area triangle CDB = (1/2)(BD)(CD)sin(angle BDC),
so sin(angle BDC) = 2(588.73169)/((60.4017164)(37.62)) = 0.51817844,
and so angle BDC = 31.210144 or 148.789856.

Now you can use the cosine rule to find the two possible values for the length of BC.
You can then use the sine rule to find angles ABD and CBD, and hence angle ABC.
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February 3rd, 2010, 02:43 AM   #6
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Re: Length of sides and angle calculations

Hi,
Thanks for the help.

I get length BC = 34.30 and angle B 74.6 deg.

Can you explain 31.210144 or 148.789856. though

Thanks...
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February 4th, 2010, 03:07 AM   #7
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Nothing in the problem requires that angle BDC is acute. How did you calculate 74.6 for angle ABC?
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