Given a triangle with b = 7, c = 3 , and A = 37° what is the length of a? Round to the nearest tenth.

I don't know I can use the law of sines with this, because the length is unavailable for the angle given. I just don't know how I can apply the law of sines to this.

Question

Given a triangle with b = 7, c = 3 , and A = 37° what is the length of a? Round to the nearest tenth.

I don't know I can use the law of sines with this, because the length is unavailable for the angle given. I just don't know how I can apply the law of sines to this.

jtvatsim · Answer

You are right! So, Law of Cosines to the rescue!

anonymous · Answer

>_< ugh how do I do that?

merchandize · Answer

Using the law of cosines:
a^2 = 7^2 + 3^2 - 2(7)(3)cos37°
a^2 = 49 + 9 - 42cos37°
a^2 = 58 - 42cos37°
a = sqrt (58 - 42cos37°)
a = 4.9

jtvatsim · Answer

$$a^2 = b^2 + c^2 - 2bc\cos{A}$$

jtvatsim · Answer

It's a mess, but that is the equation to use.

jtvatsim · Answer

It's like a modified version of the Pythagorean theorem, it works for all triangles though not just right triangles.

anonymous · Answer

Okai I think I got it c: Thank you.