Solve the triangle.

B = 36°, a = 41, c = 20

Question

Solve the triangle. 

B = 36°, a = 41, c = 20

anonymous · Answer

b ≈ 27.5, C ≈ 115.5, A ≈ 28.5

 b ≈ 45.3, C ≈ 25.5, A ≈ 118.5

 b ≈ 45.3, C ≈ 29.5, A ≈ 114.5

 b ≈ 27.5, C ≈ 25.5, A ≈ 118.5

terenzreignz · Answer

Law of Cosines?

geerky42 · Answer

Yes.

terenzreignz · Answer

You arrived at a solution, @TNNG ?

geerky42 · Answer

Use law of cosines to find b then use law of sines to find the rest of angles.

anonymous · Answer

ok so just use to law of cosines and i should get the answer

geerky42 · Answer

Well, you're not finished, since you still have to find A and C so use law of sines for this.

anonymous · Answer

i don't get it i got the D for my answer is that correct

geerky42 · Answer

What don't you get?

anonymous · Answer

the law of sines

geerky42 · Answer

The Law of Sines: $\Large \dfrac{\sin A}{a} =\dfrac{\sin B}{b} =\dfrac{\sin C}{c}$

geerky42 · Answer

Familiar with it?

anonymous · Answer

i know that but i don't get how to plug it is plus i tried it again and got Choice B

terenzreignz · Answer

Well, you could certainly use the law of Cosines to arrive at all the other missing parts of the triangle, but that's really cumbersome, compared to the simpler looking law of sines.

geerky42 · Answer

Yeah, it's only way to find the b. You just have to use it once, then use law of sines and you're good to go. You don't have to use entire formula, just use part of it, like $\dfrac{\sin B}{b} = \dfrac{\sin C}{c}$ 

Is this clear?

geerky42 · Answer

The law of tangents is really cumbersome compared to the law of cosines :P

anonymous · Answer

ok so i know b=27.5

geerky42 · Answer

Yes.

anonymous · Answer

so figure out that a = 28.5

geerky42 · Answer

No, no, you already have the given value of a, so just use law of sines to find the angle.

geerky42 · Answer

Now you know a, b, c, and B. Now all you need to do is find A and C.

anonymous · Answer

is the angle 25.5

geerky42 · Answer

None, not what I get.

anonymous · Answer

115.5

pooja195 · Answer

b^2 = a^2 + c^2 - 2accosB

b = 27.5

geerky42 · Answer

Wait, you're right, angle C is close to 25.5º. My bad.

Now find the other angle.

geerky42 · Answer

180º - (A + C) = B

anonymous · Answer

118.5

anonymous · Answer

so i had it right the first time

geerky42 · Answer

Yes!
Is this clear?

geerky42 · Answer

You have to do math, though. You can't just guess. 

Just saying.