1, solve triangle ABC which have angleA= 250.251 angleB=600.511 and a=3.82 find c
To solve triangle ABC, we can use the Law of Sines or the Law of Cosines.
1. Law of Sines: This law relates the lengths of the sides of a triangle to the sines of its angles. It states that for any triangle with sides a, b, c, and opposite angles A, B, C:
a / sin(A) = b / sin(B) = c / sin(C)
2. Law of Cosines: This law relates the lengths of the sides of a triangle to the cosines of its angles. It states that for any triangle with sides a, b, c, and angles A, B, C:
c^2 = a^2 + b^2 - 2ab * cos(C)
Given that angle A = 250.251, angle B = 600.511, and side a = 3.82, we can use the Law of Sines to find the length of side c. However, please note that the given angles are not within the normal range of 0 to 180 degrees and need to be converted.
To convert the given angles to the range of 0 to 180 degrees:
angle A = 250.251 - 180 = 70.251 degrees
angle B = 600.511 - 360 = 240.511 degrees
Now we can use the Law of Sines:
a / sin(A) = c / sin(C)
Substituting the known values:
3.82 / sin(70.251) = c / sin(C)
Now, we need to find sin(C). Since the sum of angles in a triangle is 180 degrees, we can calculate angle C.
angle C = 180 - angle A - angle B
= 180 - 70.251 - 240.511
= -130.762 degrees
To convert the negative angle to a positive angle within the range of 0 to 180 degrees:
angle C = -130.762 + 180
= 49.238 degrees
Now, we can solve for c:
3.82 / sin(70.251) = c / sin(49.238)
Rearranging the equation:
c = (3.82 * sin(49.238)) / sin(70.251)
Using a calculator, the value of c is approximately 4.680.