# Math Help - Question about GEOMETRICAL CONSTRUCTION

1. ## Question about GEOMETRICAL CONSTRUCTION

Following question is in our textbook.

Make Triangle ABC. PR = 8 cm, angle PQR = 70 degree, and AB2 + BC2 = 82 cm2 ( 2 means square )

I and also my friends are unable to solve this problem. Because of AB2 + BC2 = 82 cm2. How to make AB and BC . I hope some one will help soon. And please write the steps of constructing it. Thnx in advance....

2. Originally Posted by whyonlyme
Following question is in our textbook.

Make Triangle ABC. PR = 8 cm, angle PQR = 70 degree, and AB2 + BC2 = 82 cm2 ( 2 means square )

I and also my friends are unable to solve this problem. Because of AB2 + BC2 = 82 cm2. How to make AB and BC . I hope some one will help soon. And please write the steps of constructing it. Thnx in advance....
What is PR? And where do I find $\angle(PQR)$?

Please post the complete text of the equestion.

3. Originally Posted by earboth
What is PR? And where do I find $\angle(PQR)$?

Please post the complete text of the equestion.
I also confused because of that thing, I mean there isn't given PR and $\angle(PQR)$ . I think there is any way in AC2 +BC2 = 82.

4. Originally Posted by whyonlyme
I also confused because of that thing, I mean there isn't given PR and $\angle(PQR)$ . I think there is any way in AC2 +BC2 = 82.
In general you have

$(\overline{AC})^2+(\overline{BC})^2=82~\implies~|\ overline{AC}| = \sqrt{82-(\overline{BC})^2}$

If you are looking for $\overline{AC}$ and $\overline{BC}$ as an integer then there are only two pairs of numbers which satisfy your equation: (1, 9) or (9, 1)