Question

Solve the triangle shown to the right. (I just need my answer checked, please don't respond until I'm done)

Answer 1

1. Find Angle Beta (β)

The sum of all angles in a triangle is always 180 degrees.
We know two angles: 14.6° and 21.4°.
So, β = 180° - 14.6° - 21.4° = 144°

Now the next step is to find Side 'a' (Using the Law of Sines)

The Law of Sines states: a/sin(A) = b/sin(B) = c/sin(C)
And, we can use the known values: b = 18.2, angle B = 144°, and angle A = 21.4°

So, a/sin(21.4°) = 18.2/sin(144°)

Then, we're gonna rearrange and solve for a: a = (18.2 * sin(21.4°)) / sin(144°)
a ≈ 10.98
3. Find Side 'c' (Using the Law of Sines)

We can use the same Law of Sines like how we did before
We know b = 18.2, angle B = 144°, and angle C = 14.6°
So, c/sin(14.6°) = 18.2/sin(144°)
Rearrange and solve for c: c = (18.2 * sin(14.6°)) / sin(144°)
c ≈ 9.42
In summary:

β (Angle Beta): 144°
a (Side opposite 21.4°): 10.98
c (Side opposite 14.6°): 9.42

Answer 2

I didn't want you to do it yet, I need to solve this on my own so I can see if I understand how to do it but thank you

Answer 3

Also A and C are incorrect

Answer 4

I already got the answer though, I'll show it

Answer 5

thank you