Questions: Solve the triangle. A=36°, b=5, c=11 a= (Do not round until the final answer. Then round to the nearest tenth as needed.) B= (Do not round until the final answer. Then round to the nearest degree as needed.) C=° (Do not round until the final answer. Then round to the nearest degree as needed.)

Solve the triangle.
A=36°, b=5, c=11
a=
(Do not round until the final answer. Then round to the nearest tenth as needed.)
B=
(Do not round until the final answer. Then round to the nearest degree as needed.)
C=°
(Do not round until the final answer. Then round to the nearest degree as needed.)

Transcript text: Solve the triangle. \[ A=36^{\circ}, b=5, c=11 \] \[ \mathrm{a}= \] $\square$ (Do not round until the final answer. Then round to the nearest tenth as needed.) \[ B= \] $\square$ (Do not round until the final answer. Then round to the nearest degree as needed.) \[ \mathrm{C}=\square^{\circ} \] (Do not round until the final answer. Then round to the nearest degree as needed.)

Solution

Solution Steps

Step 1: Find side _a_ using the Law of Cosines

We are given A = 36°, b = 5, and c = 11. We can use the Law of Cosines to find side _a_:

a² = b² + c² - 2bc * cos(A) a² = 5² + 11² - 2 * 5 * 11 * cos(36°) a² = 25 + 121 - 110 * cos(36°) a² ≈ 25 + 121 - 110 * 0.809 a² ≈ 146 - 88.99 a² ≈ 57.01 a ≈ √57.01 a ≈ 7.55

Step 2: Find angle B using the Law of Sines

We can use the Law of Sines to find angle B:

sin(B) / b = sin(A) / a sin(B) / 5 = sin(36°) / 7.55 sin(B) ≈ (5 * sin(36°)) / 7.55 sin(B) ≈ (5 * 0.5878) / 7.55 sin(B) ≈ 2.939 / 7.55 sin(B) ≈ 0.3893 B ≈ arcsin(0.3893) B ≈ 22.9°

Step 3: Find angle C

The sum of angles in a triangle is 180°. We can use this to find angle C:

C = 180° - A - B C = 180° - 36° - 22.9° C ≈ 121.1°