Given , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.
E)not possible

Question

Given  , use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.
E)not possible

Quizplus · Accepted Answer

Since we are given a side and its opposite angle, we can use the Law of Sines to find the other two angles, and then use the fact that the sum of the angles in a triangle is 180 degrees to find the third angle. Then, we can use the Law of Sines again to find the remaining side.

Let c be the side opposite the given angle. Then, we have:

sin(A)/a = sin(C)/c
sin(58)/11 = sin(72)/c
c = 11(sin(72)/sin(58))
c ≈ 12.64

Now, we can use the fact that the sum of the angles in a triangle is 180 degrees to find the third angle:

180 - 72 - 58 = 50

So, we have a triangle with angles of 72, 58, and 50 degrees, and a side of length c ≈ 12.64 opposite the 72 degree angle.

To see if there are two solutions, we can use the Law of Sines again to solve for side a, opposite the 50 degree angle:

sin(50)/a = sin(72)/c
sin(50)/a = sin(72)/(11(sin(72)/sin(58)))
a ≈ 6.51 or a ≈ 19.22

So, there are two possible values for side a, and therefore two possible triangles that can be formed with the given information.

Given , Use the Law of Sines to Solve