Answer:
The two possible values of C are 64.2° and 115.8°
Step-by-step explanation:
* 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∠A = 59°
- a = 20
- c = 21
* To find the distance m∠C 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
- c/sinC = a/sinA = b/sinB
* Lets use it to find the m∠C
∵ 21/sinC = 20/sin(59)
∴ sin(C) = 21 × sin(59) ÷ 20 = 0.9000256657
∴ m∠C = sin^-1(0.9000256657) = 64.16144°
∴ m∠C = 64.2°
∵ The value of sin(C) is positive
∴ Angle C may be in the first quadrant (acute angle)
or in the second quadrant (obtuse angle)
∴ The other measure of ∠C = 180 - 64.2 = 115.8
* The two possible values of C are 64.2° and 115.8°
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