1. (2 points) Consider a person standing 12 feet from a light pole. The individual notices that the light casts a shadow of their body that is 3 feet long. If the individual is 5.5 feet tall, how tall is the light pole? (a) (1 point) Draw a diagram and label the unknown and known quantities. (b) (1 point) Determine the height of the light pole and justify your solution. 2. (4 points) True or False: the following is an identity. Assume that 9 is in radians. Justify your answer. A correct justication is necessary to receive any credit. Recall: An identity is an equation that is ALWAYS true (no matter what 6 is). If the statement is false, you can show this with one example where the equation does not hold. If the statement is true, you need to show that it is true for all values of 6'. You may justify visually with graphs. (a) sin (6 g) = cos(9) (b) cos(t9) = cos(9) 3. (4 points) Discovering a trig identity (or two!). Take a paper triangle and orient it like the one pictured. Fold the right corner up so that it i. . touches the tOp corner. Draw a line where the . edge of the folded paper rests. Unfold the paper and draw a line on the crease. Your triangle should look similar to the one on the right. (a) (2 points) i. Label all lengths and angles in the diagram that are also a, b, c, d, or 6. ii. Write an equation that relates b, c, and 6. iii. Write an equation that relates (1,3), and 6. iv. Write a: in terms of 6. (Use what you know about angles in triangles.) (b) (1 point) Write an equation for sin(:n) in terms of sin(6) and cos(0). (c) (1 point) Rewrite your equation for sin(z) replacing a: in terms of 6. What did we call this trig identity in class? (d) (2 points bonus) Write an equation that relates b, c, d, and 9. Write an equation for cos(m) in terms of cos(6) and sin(6). Finally rewrite your equation for cos(m) replacing a: in terms of 6