Solve the triangle. b = 36°, a = 42, c = 18

b = 29.4 units , m∠A = 122.9 , m∠C = 21.1°

Step-by-step 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°

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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answer: 20

step-by-step explanation: