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.

What is the magnitude 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.

Two lifeguard stations are 100 feet apart. They both spot a speedboat, which is at an angle of 60° from tower A and at 40° from tower B, when measured from the line that connects the towers. How far is the speedboat from tower A?  A physics-style diagram shows two observers at points A and B on level ground separated by 100 ft. From A, a line of sight to point C makes a 60° angle with the ground. From B, a line of sight to point C makes a 40° angle with the ground. The two lines meet at point C above the ground, forming a triangle with base AB. A dashed vertical line from C to the ground represents height d. The left side from A to C is labeled b, and the right side from B to C is labeled a.

Two lifeguard stations are 100 feet apart. They both spot a speedboat, which is at an angle of 60° from tower A and at 40° from tower B, when measured from the line that connects the towers. How far is the speedboat from tower B?  A physics-style diagram shows two observers at points A and B on level ground separated by 100 ft. From A, a line of sight to point C makes a 60° angle with the ground. From B, a line of sight to point C makes a 40° angle with the ground. The two lines meet at point C above the ground, forming a triangle with base AB. A dashed vertical line from C to the ground represents height d. The left side from A to C is labeled b, and the right side from B to C is labeled a.

What is the approximate area of 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.