Q:

URGENT ANSWER NOW In △ABC, A=59∘, a=20, and c=21. What are the two possible values for angle C to the nearest tenth of a degree? Select both correct answers.Select all that apply:C=111.8∘C=115.8∘C=66.2∘C=113.8∘C=68.2∘C=64.2∘

Accepted Solution

A:
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°