the length of the side ‘a’ is √3.
To find the length of the side ‘a’ in a triangle given the length of one side ‘c’ and two angles ‘A’ and ‘B’, we can use the Law of Sines.
The Law of Sines states that:
sin(A) / a = sin(B) / b = sin© / c
where A, B, and C are the angles of the triangle, and a, b, and c are the lengths of the corresponding sides.
Given information:
Side c = 2
Angle A = π/4 (45 degrees)
Angle B = π/6 (30 degrees)
Step 1: Calculate the third angle C using the fact that the sum of the angles in a triangle is 180 degrees. A + B + C = 180 degrees π/4 + π/6 + C = π C = π - (π/4 + π/6) C = π - 5π/12 C = 7π/12 (105 degrees)
Step 2: Use the Law of Sines to find the length of side a. sin(A) / a = sin(B) / c sin(π/4) / a = sin(π/6) / 2 a = (2 × sin(π/4)) / sin(π/6) a = (2 × √2/2) / (√3/2) a = √3
Therefore, the length of the side ‘a’ is √3.
