Solve the triangle.Round lenghts to the nearest tenth and angle measurements to the nearest degree. B = 43 C = 107 B = 14

you gave

B = 43 C = 107 B = 14

What does that mean, are they angles or lengths of sides.
Please be more specific.

knowing these kind of questions, I will assume that 14 units is the length of the side opposite the 43º angle.
then the third angle is 30º and by the Sine Law

c/sin107 = 14/sin43

cross-multiply and solve for c

in the same way a/sin30 = 14/sin43

Thanks I'm sorry for not being more specific I'm new to this site. Thanks for your help.

To solve a triangle, we need to first find the third angle (angle A), and then we can use the Law of Sines or the Law of Cosines to find the remaining side lengths.

Step 1: Find angle A
Angle A can be calculated by subtracting the sum of the other two angles (B and C) from 180 degrees.
A = 180 - (B + C)
A = 180 - (43 + 107)
A = 30 degrees

Step 2: Find the remaining side lengths using the Law of Sines or the Law of Cosines.
Since we have the angles and one side-length, we can use the Law of Sines to find the remaining side lengths.

The Law of Sines states that for any triangle:
a/sin(A) = b/sin(B) = c/sin(C)

Given:
B = 43 degrees
C = 107 degrees
b = 14 (opposite side of angle B)

Using the Law of Sines, we can find side a as follows:
a/sin(A) = b/sin(B)
a/sin(30) = 14/sin(43)
a = (14 * sin(30)) / sin(43)
a ≈ 8.4

Similarly, we can find side c as follows:
c/sin(C) = b/sin(B)
c/sin(107) = 14/sin(43)
c = (14 * sin(107)) / sin(43)
c ≈ 23.4

Therefore, the side lengths are approximately:
a ≈ 8.4
b = 14
c ≈ 23.4

And the angles are:
A ≈ 30 degrees
B = 43 degrees
C = 107 degrees

To solve the triangle, we can use the Law of Sines or the Law of Cosines. Since we have two angles and one side, it is more appropriate to use the Law of Sines in this case. The Law of Sines states that the ratio of the length of a side to the sine of its opposite angle is constant for all sides of a triangle.

To find the missing side lengths, let's label the triangle ABC, with angle A being the remaining angle. Given that B = 43 degrees, C = 107 degrees, and b = 14, we can set up the Law of Sines equation:

a / sin(A) = b / sin(B) = c / sin(C)

Substituting the given values:

a / sin(A) = 14 / sin(43) = c / sin(107)

To find side a, we rearrange the equation:

a = (14 * sin(A)) / sin(43)

To find side c, we rearrange the equation:

c = (14 * sin(107)) / sin(A)

Now, we need to find angle A using the fact that the sum of the angles of a triangle is 180 degrees:

A = 180 - B - C

Substituting the given values:

A = 180 - 43 - 107

A = 30 degrees

Now that we have angle A, we can use this value to calculate the missing side lengths:

a = (14 * sin(A)) / sin(43)

a = (14 * sin(30)) / sin(43)

a ≈ 8.7 (rounded to the nearest tenth)

c = (14 * sin(107)) / sin(A)

c ≈ 10.9 (rounded to the nearest tenth)

So, the lengths of the sides of the triangle are approximately a = 8.7 and c = 10.9, and angle A is approximately 30 degrees.