Math Is Fun Forum

parseconds

Member

Registered: 2008-05-13

Posts: 3

Quadrilateral

Consider the quadrilateral ABCD pictured below.  The three sides AD, DC, and CB have lengths 50, 60, 70 respectively.  Angle <C measures 132

and <ADC measures 127

.

a) Find the length of DB and the measure of angles <BDC and <ADB.

b) Find the area of the quadrilateral (recall

)

c) Find the length of side AB and the measure of angle <BAD

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Quadrilateral

This is all done with trigonometry. Apart from when you're given a formula to use, you can do everything using just these two formulas:

The Sine Rule

The Cosine Rule

In both of these, each angle in a triangle is paired with the side of the triangle that doesn't form part of it, and they're given matching letters.

In both formulas, four pieces of information are involved: side lengths and angles. If you know three bits of information, then you can use the formulas to find the 4th one.

Use the Sine Rule when working with 2 sides and 2 angles.
Use the Cosine Rule when working with 3 sides and 1 angle.

So for a), the first thing you need to find is DB. That's a side length, and you also know two other side lengths and an angle, so you use the Cosine Rule.
In this case, the length you want corresponds to the angle you know, so the formula looks like this:

This gives DB = 118.8 (roughly).
For the two other angles, you then use the Sine Rule along with the piece of information you just found.
c) is done in a similar way, and b) is even easier because you're told the formula you need.

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Why did the vector cross the road?
It wanted to be normal.