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Geometry 2: Trigonometry Unit Review Name ______________________________________ Period _______________ Date _________________ G.SRT.6 Learning Target: Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute ratios. 4) Darren started with a 5-12-13 right triangle ( HKI ) and then reflected it horizontally to get a congruent triangle, JKI . The length of HK 1) Given the following trig ratios, what is the length of AC? is 5 cm. A C 36 12 13 5 cos A 13 12 tan A 5 sin A B H K J Answer: ______________ 2). Complete the following trig ratios for I ACB Then, Darren claimed the following: - Since HK is 5 cm, then JK is also 5 cm. and KI is 12 cm. - Using the Pythagorean Theorem, the length of HI and JI is 13 cm. - The length of HJ is 10 cm. - Therefore, tan ( IHK ) = 5 0.42 12 (rounded) sin A = cos A = 3) Given ABO = 20, what is the length of LK? Answer: ______________ tan A = KLJ . If the cos A = 0.6 and JK Sadly, Darren went wrong somewhere in his assumptions. Find his mistake and correct it. _______________________________________ _______________________________________ _______________________________________ _______________________________________ _______________________________________ G.SRT.7 Learning Target: Explain and use the G.SRT.8 Learning Target: Use trigonometric relationship between the sine and cosine of complementary angles. ratios and the Pythagorean Theorem to solve right triangles in applied problems 5. Write sin 50° in terms of cosine. Then, explain how cosine and sine are related in a given triangle. Answer: _______ 8) Which expression(s) can be used to find the value of x in the triangle? There may be more than one. Explanation: __________________________________________ __________________________________________ __________________________________________ __________________________________________ (a) cos 59 6) In the right triangle ABC, A and B are complementary angles. Which statement is TRUE? C 20 48 A B (b) cos 59 x 14 14 (c) sin 59 x x (d) sin 59 14 (e) sin 31 52 14 x 14 x (f) tan 59 14 a) The cos A and the sin B are both equal to x 12 . 13 5 b) The cos A= 12 and the sin B = . 13 13 c) The cos A and the sin B are both equal to 5 13 5 12 d) The cos A= and the sin B = . 13 13 Answer: ______________ 7). What is the solution to the following equation? Round your answer to the nearest tenth. cos (2x + 18)° = sin (4x + 5)° Answer: ______________ Answer(s)______________ 9). Which expression CANNOT be used to find the length of LM ? (a) tan 55 8.6 x (b) sin 35 = x 8.6 (c) cos 55 = x 12.5 (d) tan 35 x 8.6 Answer: ________ 10) A tower is anchored to the ground by a wire. How far away is the wire from the base of the tower if it is attached to the top of a 50-ft antenna and makes a 70° angle with the ground? Round to the nearest tenth. 12) If the length of each side of the square sign shown below is 15 inches, how long is the diagonal? (Round to the nearest inch.) Answer: ______________ 11). You are flying a kite!! The angle of depression is 23º. If your eyes are five feet high, how high off the ground is the kite? Round your answer to the nearest tenth. Answer: ________________ Answer: ________________