The point (a,b) shown below represents which complex number?  A complex number plane is shown with the horizontal axis labeled “Real” and the vertical axis labeled “Imaginary.” The grid is marked from −10 to 10 on the imaginary axis and from −5 to 5 on the real axis. A red point appears in the second quadrant at approximately (−2, 5). The point is labeled “(a, −b)” in red text. The location indicates a negative real part and a positive imaginary part.

What is the approximate measure of angle A on triangle ABC? A triangle labeled A, B, and C is shown. Points A and B are connected by a horizontal top side labeled 8 in. Point C is below between them, forming an inverted triangular shape. The side from A to C is labeled 4 in., and the side from C to B is labeled 6 in. The triangle is scalene, with all three sides having different lengths.

Find the measure of angle D. A triangle with vertices labeled R, A, and D is shown. Vertex R is on the left and D is on the right, connected by a horizontal base RD labeled 9. Vertex A is above the base, forming the top of the triangle. Side RA is labeled 7, and side AD is labeled 5. The triangle is scalene and drawn with straight black line segments on a plain background.

Find the measure of angle N.  A scalene triangle with vertices labeled F, U, and N is shown. Vertex F is on the left, U is at the upper right, and N is at the lower right. Side FU is labeled 2, and side FN is labeled 5. The angle at vertex F measures 86°. Side UN is drawn as a vertical segment connecting U and N. The triangle is formed by straight black line segments on a plain background.

Adriana, Drew, and Juan are playing catch a baseball. Drew is standing 60 feet from Adriana and 57 feet from Juan. The angular distance between Adriana and Juan from where Drew is standing is 105°.  What is the distance between Adriana and Juan?

What is the component form of the vector shown?  A coordinate grid is shown with x- and y-axes labeled from −5 to 5. A solid point appears in the first quadrant, approximately at (2, 3). From this point, a line segment with an arrow extends downward and slightly left, ending in the fourth quadrant around (0, −2). The arrow indicates direction from the upper-right point toward the lower area near the y-axis.

If  , which quadrant(s) is the terminal side of  in? Select all that apply. 

What is the area of the triangle shown?  A triangle with vertices labeled A, B, and C is shown. Vertex A is on the left, C is on the right along a horizontal base, and B is above between them. Side AB is labeled 10. The angle at A measures 42°, and the angle at B measures 105°. The sides are drawn with straight black segments, and no coordinate grid is present.

If  and  , find .

Which are valid identities? Select all that apply.