Author: Anonymous

Which is a valid trigonometric identity? 

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.

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 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.

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 angular distance between Juan and Drew from where Adriana is standing?

Cormac walks 5 km due east, 4 km due south, and 3 km due west. Which vector represents his total displacement? 

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.

Which is the direction angle of the vector  ?

What is the area of the triangle shown?  A triangle with vertices labeled E, F, and G is shown. Vertex E is at the upper left, F is at the lower left, and G is to the right. The side from F to G is labeled e = 18. The angle at F measures 60°, and the angle at G measures 45°. The sides are drawn with straight black segments, forming a scalene triangle on a plain background.

Which are valid identities? Select all that apply.