Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 29°, b = 14, c = 29
A)a ≈ 18.08, B ≈ 22.05°, C ≈ 128.95°
B)a ≈ 29, B ≈ 24.05°, C ≈ 126.95°
C)a ≈ 18.08, B ≈ 128.95°, C ≈ 22.05°
D)a ≈ 14, B ≈ 22.05°, C ≈ 128.95°
E)a ≈ 29, B ≈ 22.05°, C ≈ 128.95°

Question

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places.  A = 29°, b = 14, c = 29 ​
A)a ≈ 18.08, B ≈ 22.05°, C ≈ 128.95° 
B)a ≈ 29, B ≈ 24.05°, C ≈ 126.95° 
C)a ≈ 18.08, B ≈ 128.95°, C ≈ 22.05° 
D)a ≈ 14, B ≈ 22.05°, C ≈ 128.95° 
E)a ≈ 29, B ≈ 22.05°, C ≈ 128.95°

Quizplus · Accepted Answer

Applying the law of cosines, we have:

a^2 = b^2 + c^2 - 2bc cos(A)
a^2 = 14^2 + 29^2 - 2(14)(29)cos(29°)
a ≈ 18.08

Now, we can use the law of sines to find the other angles:

sin(B)/b = sin(A)/a
sin(B) = (b/a)sin(A)
sin(B) ≈ (14/18.08)sin(29°)
B ≈ 22.05°

Finally, we can find angle C by using the fact that the sum of angles in a triangle is 180°:

C ≈ 180° - A - B
C ≈ 128.95°

Use the Law of Cosines to Solve the Given Triangle