Please i need help ASAP
pls explain your answer

Step-by-step explanation:

Challenging question!

Start by constructing a square in the lower-left quadrant of the circle (that isn't shaded) that is tangent to center C, OP, and OQ:

(See picture)

With the blue line constructed, we can conclude that the blue line (the blue line is the measure from the center of the inscribed circle to the center of the quarter circle) measures due to the Pythagorean theorem.

The orange line is the radius of the inscribed circle, so adding the blue line and the orange line gives the radius of the quarter circle, so:

Solve the equation with a bit of algebra to get:

Now, we will find the area of the inscribed circle:

And we will now find the area of the quarter circle...:

...and we subtract both results...:

To get the area of the shaded region.

Not sure what does the last part ("correct to 3 s. f.") meant but that's all I can do.

(sin 42)/31. = sinx)/37

sinx = 37 (sin42)/31

= 37× 0.66/31 = 0.787

x= 51.9

other angle opposite to y = 180-51.9-42

= 180- 93.9 =86.1

so

sin42)/31 = sin 86.1)/y

0.021 = 0.997 /y

y= 0.997/0.021 =47.47

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation: