Answer:
b = 29.4 units , m∠A = 122.9 , m∠C = 21.1°
Explanation:
* To solve a triangle we can use cosine rule and sin rule
* In ΔABC
- If a, b, c are the lengths of its 3 sides, where
# a is opposite to angle A
# b is opposite to angle B
# c is opposite to angle C
- By using the cosine rule:
# a² = b² + c² - 2bc cos(A)
# b² = a²² + c² - 2ac cos(B)
# c² = a² + b² - 2ab cos(C)
- By using sin rule
# c/sinC = a/sinA = b/sinB
* Lets solve the problem
∵ a = 42 , c = 18 , m∠B = 36°
* We will use the cosine rule
∴ b² = (42)² + (18)² - 2(42)(18) cos(36) =864.766 ⇒ take √ for both sides
∴ b = 29.4
* Now we will use the sin rule to find m∠C
∵ 29.4/sin(36) = 18/sin(C) ⇒ by using cross multiplication
∴ sin(C) = 18 × sin(36°)/29.4 = 0.3598685
∴ m∠C = 21.1°
* The sum of the measure of the interior angle of a triangle is 180°
∴ m∠A = 180° - (36° + 21.1°) = 122.9°
* b = 29.4 units , m∠A = 122.9 , m∠C = 21.1°