Refer to the figure and use the given information to solve the triangle. Round angles to the nearest degree and side
lengths to one decimal place.
-b = 7.5, c = 14.9
A) A = 45, B = 45, C = 90, a = 13.2, b = 7.5, c = 14.9
B) A = 30, B = 60, C = 90, a = 12.6, b = 7.5, c = 14.9
C) A = 60, B = 30, C = 90, a = 12.9, b = 7.5, c = 14.9
D) A = 60, B = 30, C = 90, a = 11.4, b = 7.5, c = 14.9

Question

Refer to the figure and use the given information to solve the triangle. Round angles to the nearest degree and side
lengths to one decimal place. 
-b = 7.5, c = 14.9
A) A = 45, B = 45, C = 90, a = 13.2, b = 7.5, c = 14.9 
B) A = 30, B = 60, C = 90, a = 12.6, b = 7.5, c = 14.9 
C) A = 60, B = 30, C = 90, a = 12.9, b = 7.5, c = 14.9 
D) A = 60, B = 30, C = 90, a = 11.4, b = 7.5, c = 14.9

Quizplus · Accepted Answer

Using the Law of Cosines, we can solve for the unknown side length a:
a^2 = b^2 + c^2 - 2bc*cos(A)
a^2 = (7.5)^2 + (14.9)^2 - 2(7.5)(14.9)*cos(A)
a^2 = 56.25 + 222.01 - 223.5*cos(A)
a^2 = 55.76
a = 7.5

Then, we can use the Law of Sines to solve for the remaining angles:
sin(A)/a = sin(C)/c
sin(A)/7.5 = sin(90)/14.9
sin(A) = 7.5/14.9
A = 29.7 (rounded to nearest degree)

Using the fact that A + B + C = 180, we can solve for angle B:
B = 180 - A - C
B = 180 - 29.7 - 90
B = 60.3 (rounded to nearest degree)

Therefore, the triangle is a 30-60-90 triangle, with side lengths a = 12.9, b = 7.5, and c = 14.9. So, the best choice is C. Using the Law of Cosines, we can solve for angle A:
a^2 = b^2 + c^2 - 2bc*cos(A)
a^2 = 7.5^2 + 14.9^2 - 2*7.5*14.9*cos(A)
a^2 = 178.52 - 223.5*cos(A)
cos(A) = (178.52 - a^2 - 223.5)/(-2*7.5*14.9)
cos(A) = -0.3702
A = arccos(-0.3702)
A = 109.5 degrees

Since the sum of the angles in a triangle is 180 degrees, we can solve for angle B:
B = 180 - 90 - A
B = 180 - 90 - 109.5
B = -19.5

However, we know that angle B must be acute (less than 90 degrees). This means that Triangle ABC is obtuse and we must use the acute angle opposite c (14.9) as angle A. Therefore, we have:
A = 60 degrees
B = 30 degrees

Using the Law of Sines, we can solve for side a:
a/sin(A) = c/sin(C)
a/sin(60) = 14.9/sin(90)
a = 14.9*sin(60)
a = 12.9

Therefore, the best choice is C: A = 60, B = 30, C = 90, a = 12.9, b = 7.5, c = 14.9.

Refer to the Figure and Use the Given Information to Solve