# Thread: find lengths of triangle's 2 sides

1. ## find lengths of triangle's 2 sides

hi

The perimeter of triangle ABC = 15 cm. Given that AB = 7 cm and angle BAC = 60 degreez, find the lengths of AC and BC.

Anyone could give me some hint how to go with this ? Because all i know is that b+c=8 ..

2. ## Re: find lengths of triangle's 2 sides

Originally Posted by AbYz
hi

The perimeter of triangle ABC = 15 cm. Given that AB = 7 cm and angle BAC = 60 degreez, find the lengths of AC and BC.
Anyone could give me some hint how to go with this ? Because all i know is that b+c=8 ..
The rule of cosines tells us that
$(8-b)^2=b^2+49-7b\cos(60^o)$

3. ## Re: find lengths of triangle's 2 sides

Originally Posted by Plato
The rule of cosines tells us that
$(8-b)^2=b^2+49-\color{red}{2} \cdot 7b\cos(60^o)$
...

method 2 ... use Pythagoras on the larger right triangle

4. ## Re: find lengths of triangle's 2 sides

Originally Posted by AbYz
Anyone could give me some hint how to go with this ? Because all i know is that b+c=8 ..
You didn't know that COS(60) = 1/2 ?

5. ## Re: find lengths of triangle's 2 sides

Originally Posted by DenisB
You didn't know that COS(60) = 1/2 ?
somehow i ruled out using sine/cosine rules at the beginning..