Answer:
To solve the triangle, we can start by using the Law of Sines to find the other two angles:
a/sin A = b/sin B = c/sin C
We know B = 60°, C = 40°, and b = 7, so we can solve for a and c:
a/sin A = 7/sin 60°
a = (7 sin A)/sin 60°
c/sin 40° = 7/sin 60°
c = (7 sin 40°)/sin 60°
Next, we can use the fact that the three angles of a triangle add up to 180° to solve for A:
A + B + C = 180°
A + 60° + 40° = 180°
A = 80°
Now we have all three angles of the triangle and can use the Law of Sines again to find the remaining sides:
a/sin A = b/sin B = c/sin C
a/sin 80° = 7/sin 60°
a = (7 sin 80°)/sin 60° ≈ 8.09
c/sin 40° = 7/sin 60°
c = (7 sin 40°)/sin 60° ≈ 5.47
Therefore, the solution for the triangle is:
A = 80°, B = 60°, C = 40°
a ≈ 8.09, b = 7, c ≈ 5.47
Note that we can check our solution using the Law of Cosines:
c^2 = a^2 + b^2 - 2ab cos C
(5.47)^2 = (8.09)^2 + (7)^2 - 2(8.09)(7) cos 40°
23.77 ≈ 23.77
This confirms that our solution is correct.
Explanation:
please follow me for more if you need any help