In right triangle JFK sin (52) = cos (5x-2). What is the measure of the smallest angle in the triangle?

48°

Step-by-step explanation:

Given the trigonometry equation

sin (52) = cos (5x-2) ... 1

According to the quadrant:

Sin (θ) = cos (90-θ)

Sin52 = cos (90-52)

Sin52 = cos48 ... 2

Substituting 2 into 1:

Cos48 = cos (5x-2)

48 = 5x-2

5x = 48+2

5x = 50

x = 10°

The smallest of the angle will be angle 5x-2 = 5 (10) - 2

= 50-2

= 48°