Question

In rectangle ABCD, BD=12 and m angle ABD=30 degrees. What is the length of the longer side of the rectangle?

Answer 1

The figure above shows the given information.

Answer 2

We know that angles between the sides is 90deg
If u draw the diagram...u see that a right angled triangle Whose hypotenuse is the length of the diagonal that is 12 and by using simple trigonometry u can find the measure of the longer side if the triangle

Answer 3

So you mean like sin tan and cosine? I'm never sure which one to use.

Answer 4

How would I set up the equation?

Answer 5

How to draw the diagram? Can't explain cos I don't know

Answer 6

In the diagram...
Llet theta be 30 deg
BAD is a right angled triangle...
Therefore cos (theta)=(AB/12)
Therefore cos30=AB/12

Answer 7

Oh okay so AB would be \[6\sqrt{3}\]

Answer 8

There is a different way without trig.

Answer 9

Since this is a rectangle, each vertex is at a 90 degree angle.
That means we have a 30-60-90 triangle.
The ratio of the lengths of the sides of a 30-60-90 triangle is:

\(1 : \sqrt{3} : 2\)

That means that the hypotenuse is twice the length of the short leg, and the long leg is \(\sqrt 3\) times longer than the short leg.

We know the hypotenuse is 12.
That makes the short leg half of 12 or 6.
The long leg is \(\sqrt 3\) times longer than the short leg, so the long leg is
\(6 \sqrt 3\) which is what we were asked for.