cosine/sine law-- help please

[rabia]

question is:

A cottage under construction is to be 15.6 m wide. The two sides of the roof are to be supported by equal rafters that meet at a 52 degree angle. Determine the length of the raters to the nearest cm using (i) cosine Law and (ii) Sine Law.

what i am having trouble with is that since we are only given one length and one angle how can we apply the two laws. We need more information. Also i think to start this question we would have to find the angles first that can be done by using the 180 degree rule since the two sides of the roof are equal the angles of them would be 64 degress each but them i am not sure what to do from there.. Please Help me

[attachment=0]quest # 62.JPG[attachment]

 

[mmm4444bot]

… what i am having trouble with is that since we are only given one length and one angle how can we apply the [Law of Sines] …

You now have two angles. You also know the length opposite one of these angles, and you're asked to find the length opposite the other angle.

Use the Law of Sines to write a proportion.

x = the unknown length

\(\displaystyle \frac{sin(64^{\circ})}{x} = \frac{sin(52^{\circ})}{15.6}\)

Please show your work, if you would like more help with this.

 

[rabia]

ok so if i use Sine law then i would get the result of

x = 15.6Sin 64
[sub:rztywe7k][/sub:rztywe7k]Sin 52
x = 17.79

how about the consine law..how would i use that

a^2 = b^2 + c^2 - 2abCOS A

is this the forumla i am using..??

and thanks for your help also

 

[mmm4444bot]

… x = 17.79 … I would report the answer as 17.8 meters (i.e., include the units).

… how would i use [the Law of Cosines] … See post below.

We use the Law of Cosines when we know TWO lengths and the angle BETWEEN them.

a^2 = b^2 + c^2 - 2abCOS A This is wrong; look up the Law of Cosines in your textbook.

MY EDIT: Corrected comment about using Law of Cosines

 

[mmm4444bot]

Actually, if we realize that both unknown lengths are EQUAL, then we could use the Law of Cosines, as follows.

\(\displaystyle 15.6^2 = x^2 + x^2 - 2(x)(x) \cdot cos(52^{\circ})\)