I posted this question about an hour ago, got a response but still confused.
Use the Law of Sines to solve for all possible triangles that satisfy the given conditions. (If an answer does not exist, enter DNE. Round your answers to one decimal place. Below, enter your answers so that ∠B1 is smaller than ∠B2.)
a = 34, c = 43, ∠A = 39°
∠B1 =
°
∠B2 =
°
∠C1 =
°
∠C2 =
°
b1 =
b2 =
This is the answer I received
sinC/c = sinA/a
sinC/43 = sin39°/34 = 0.01851
sinC = .7959
so, C = 52.74° or 127.26°
Since A+B+C=180, B=88.26° or 13.74°
Now use those two values for B to get B, using
b/sinB = 1/0.01851 = 54.0265
I am still trying to figure out how to solve for b1. I am confused as to how they got the 1 and why they used 0.01851 when they said to use the two values for B to get B (the two values are 88.26 and 13.74)
To solve for b1, we can use the Law of Sines again.
First, let's recap the information we have:
Side a = 34
Side c = 43
Angle A = 39°
We have already calculated that angle C can be either 52.74° or 127.26°, and angle B can be either 88.26° or 13.74°.
Now let's focus on finding b1 using the information we already have:
We can use the formula b/sinB = c/sinC to find b1.
sinC = 0.7959
Let's consider the case when B = 88.26°:
b1/sin(88.26°) = 43/sin(52.74°)
Now, we need to rearrange the equation to solve for b1:
b1 = (sin(88.26°) * 43) / sin(52.74°)
Calculating this value, we find that b1 is approximately equal to 54.0265.
Now, let's consider the case when B = 13.74°:
b1/sin(13.74°) = 43/sin(127.26°)
Again, we rearrange the equation to solve for b1:
b1 = (sin(13.74°) * 43) / sin(127.26°)
Calculating this value, we find that b1 is approximately equal to 13.9724.
So, the possible solutions for b1 are approximately 54.0 and 14.0 (rounded to one decimal place).
I apologize for the confusion caused by the previous answer's mention of using 0.01851. It seems to be an error in their explanation. The correct approach is to use the values of sin and rearrange the equation as shown above.