Question

What is the measure of angle C, to the nearest degree? (Image Attached)

a. 22*
b. 43*
c. 47*
d. 68*

Answer 1

Answer: (B) - 43°
Explanation: Using the sine rule, we can say that sinA/BC = sinC/AB
sin(61)/45 = sin(C)/35
sin(C) = 35sin(61)/45

sin(C) ≈ 0.680259772....
C = arcsin(0.680259772...)

C = 42.8639459...
C ≈ 43°

Answer 2

((B)

Explanation:

From the figure, it is given that ABC is a triangle and AB=35 and BC=45.

Now, from ΔABC, using the sine law, we get

`(sinA)/(BC)=(sinC)/(AB)`

Substituting the given values, we get

`(sin61^(\circ))/(45)=(sinC)/(35)`

`sinC=(35*(sin61))/(45)`

`sinC=(35*(0.874))/(45)`

`sinC=(30.611)/(45)`

`sinC=0.680`

`C=sin^(-1)(0.680)`

`C=42.84`

`C`≈
`43`

Thus, the measure of angle C is 43.

Hence, option (B) is correct.