Answer:
m∠A = 76° , m∠C = 68° , a = 31.4
Step-by-step explanation:
* Lets revise how to solve a triangle
- In ΔABC
- 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
- m∠B = 36°
- b = 19
- c = 30
* To solve the triangle we can use the sin Rule
- In any triangle the ratio between the length of each side
to the measure of each opposite angle are equal
- a/sinA = b/sinB = c/sinC
* Lets use it to find a and m∠C
∵ m∠B = 36° , b = 19 and c = 30
∵ 19/sin36° = 30/sinC ⇒ by using cross multiplication
∴ sinC = 30 × sin36° ÷ 19 = 0.928
∴ m∠C = sin^-1(0.928) = 68°
- Find measure of angle A
∵ The sum of the measures of the interior angles in a triangle is 180°
∵ m∠A = 180° - (68° + 36°) = 180° - 104° = 76°
∴ m∠A = 76°
- Now we can Find a
∵ a/sinA = b/sinB
∴ a/sin76° = 19/sin36° ⇒ by using cross multiplication
∴ a = 19 × sin(76°) ÷ sin(36°) = 31.4
* m∠A = 76° , m∠C = 68° , a = 31.4
