Question

Solve the triangle shown to the right.

Answer 1

Angles:
One angle is 18.2°
Another angle is 28.2°

Sides:
One side (b) is 17.8 units long.
What we need to find:

The third angle (β)
The lengths of the other two sides (a and c)
Here's how we'll do it:

Find the third angle (β):

The angles in a triangle always add up to 180°.
β = 180° - 18.2° - 28.2° = 133.6°
Find side a and side c:

Then, we gotta use the Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)

Finding side a:

a / sin(18.2°) = 17.8 / sin(133.6°)
a = (17.8 * sin(18.2°)) / sin(133.6°) ≈ 8.16
Finding side c:

c / sin(28.2°) = 17.8 / sin(133.6°)
c = (17.8 * sin(28.2°)) / sin(133.6°) ≈ 10.9

Solution:

β = 133.6°
a ≈ 8.16
c ≈ 10.9

Answer 2

I think it'll be better if I write it out because looking at it this way will make it more confusing so I'm going step by step but thank you <3

Answer 3

I'm going step by step on it

Answer 4

Answer
The answer is $$\beta = 133.6^{\circ }$$

and $$\alpha + \gamma = 46.4^{\circ }$$

Answer 5

So here we're gonna combine the numbers:

2 + 28.2 = 46.4
So, the equation becomes: 46.4 + B = 180

Then, we're gonna isolate B:

Subtract 46.4 from both sides of the equation:

B = 180 - 46.4

Finally, Calculate the result:

B = 133.6

Answer: The value of B (Beta) is 133.6

Answer 6

@thatcreepyboy do you have any other ones?

Answer 7

I didn't write it for this but a will be 7.7