Math Is Fun Forum

haftakhan

Member

Registered: 2010-06-28

Posts: 30

Constructing a Kite

How to construct a kite PQRS where PQ=QR=3.6 cm ,PS=6.9cm and PQR=124 degree

Find the diagonals PR and QS

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Constructing a Kite

Hi Haftakhan,

A kite has two pairs of adjacent (next to) sides equal so SR must be 6.9 as well.

The line QS must be a line of symmetry and the diagonals cross at 90 degrees.

(i) Start by drawing a line and mark Q at one end.  (see diagram)

(ii) Measure with a protractor 62 degrees each side of this line and measure 3.6 to mark P and R.

(iii) Set a compass to 6.9 and with centre P draw an arc to cut the first line at S.

If your questioner wants a measured answer for the diagonals, that's now straight forward.

If you want a calculated answer, call the point where the diagonals cross T.

Use trigonometry PT/PQ = sine 62 to calculate PT and double it to get PR.

Then calculate QT ( = PQ x cosine62).

And TS by Pythagoras (you know PS and PT now).

Add QT + TS to get QS.

Bob

Last edited by Bob (2010-08-14 00:01:57)

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Constructing a Kite

Hi haftakhan;

The diagonals are perpendicular to one another.
The shorter diagonal is bisected by the longer diagonal.
The kite is symmetrical about the longer diagonal.
The longer diagonal bisects the angles at each end of the diagonal.

Using those you can draw this. From that diagram you should now be able to get PR and QS using trigonometry and pythagorean theorem.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Constructing a Kite

Hi bobbym

After your 'Introductions' comment "No, not me. I hate resting. But if you must then..." I thought I had proof that you never sleep.

But I finally managed to get in a reply before you by 78 seconds!

For me, this is a small (and very petty) triumph.

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Constructing a Kite

Hi bob bundy;

May you have many more! Nice to see you.

I was just giving him a little help.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,583

Re: Constructing a Kite

Hi bobbym

Thanks and nice to see you too.  I'm going to track down that nasty integral post and ask a question there.

bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob