Answer:
Explanation:
This is a triangle with sides 15.2 cm, 6.6 cm, and 15.6 cm. To solve for the angles, we can use the Law of Cosines:
c^2 = a^2 + b^2 - 2ab cos(C)
where a = 6.6 cm, b = 15.6 cm, c = 15.2 cm, and C is the angle opposite side c.
Using this formula, we can solve for the cosine of angle C:
cos(C) = (a^2 + b^2 - c^2) / 2ab
cos(C) = (6.6^2 + 15.6^2 - 15.2^2) / (2 * 6.6 * 15.6)
cos(C) = 0.748
Taking the inverse cosine of 0.748, we get:
C = 41.5 degrees
To find the other angles, we can use the Law of Sines:
a/sin(A) = b/sin(B) = c/sin(C)
Using this formula, we can solve for angle B:
sin(B) = (b/sin(C)) * sin(A)
sin(B) = (15.6/sin(41.5)) * sin(A)
sin(B) = 0.614 * sin(A)
Using the fact that sin(A) + sin(B) + sin(C) = 1, we can solve for sin(A) and sin(B):
sin(A) = (sin(C) - sin(B)) / (1 + cos(C))
sin(A) = (sin(41.5) - 0.614 * sin(A)) / (1 + cos(41.5))
Solving for sin(A), we get:
sin(A) = 0.266
Using this value of sin(A), we can solve for sin(B):
sin(B) = 0.614 * sin(A)
sin(B) = 0.157
Taking the inverse sine of these values, we get:
A = 15.4 degrees
B = 123.1 degrees
Therefore, the triangle has angles of approximately 15.4 degrees, 123.1 degrees, and 41.5 degrees.