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

Solution:

To find the angle C, the law of sines formula is used, it is the ratio of the length of the side of the triangle to the sine of the angle thus formed between the other two remaining sides, given by,

sinA / a = sinB / b = sinC / c

where, a, b, and c are the lengths of the triangle and A, B, and C are the angles of the triangle.

Given ∠A = 61°, c = 35, a = 45

∴( sinA)/a = (sinC)/c

(sin 61° )/ 45 = (sin C) / 35

sin c = ((sin 61°) / 45) × 35

sin c = 0.68

c ≈ 42.8°

What is the measure of angle C, to the nearest degree? 

Summary:

The measure of angle C of the given triangle is 42.8°.