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station l: pgthagorean Theorem and Rationalizing Denominators = ladder 25 feet long is leaning against a wall 20 feet up the wall. How far is the bottom of the ladder from the hm of the wall? 1. Draw it 2. Show all work to support your answer -z 20 2 4 X . In the accompanying diagram of right triangles ABDand DBC,AB 5, AD 4, and CD— l. Find the length of BC, leave answer in simplest radical form. Write the following expression so that each denominator is a rational number. Simplify completely. station L: SOHCAHTOA- CALCVLAIOR in Which ratio represents the cosine of angle A in the right triangle below? 1) 3 4) 4 In triangle MCT,the measure of Z T = 900, MC = 85 em, CT= 84 em, and Tl'f= 13em. Which ratio represents Hint: DRAW IT!) 85 84 85 84 13 The diagram below shows right triangle LMP. Which ratio represents the angent of Z PIM? Which equation shows a correct trigonometric ratio for angle A in the right triangle below? sinA tanA — 17 cm 15 cm sine Complete both Column A AND Column B: ColumnA for the value of x, to the nearest tenth. 16 Column B 4. Solve for the nt4B to the nearest hundredth of a degree c .4 x IC co c ;' ((0s9) 27 16 2. You go to the park on a windy day to fly a kite. You have released 40 feet of string. The string makes an angle of 360 with the ground. How high is the kite in the air to the nearest foot? 5. A ladder is resting against le eo a 111Ing. The bottom of the ladder is 12 feet from the building, and the ladder reaches 7 feet up the side of the building. Find the measure of the angle of elevation, to the nearest tenth of a degree. -1 HO K qosin(3G) 30t3 ee casts a 25-foot shadow on a sunny day, as shown in the diagram below 6. The diagram below shows the path a bird flies from the top of a 9.5 foot tall sunflower to a point on the ground 5 feet from the base of the sunflower. s O 5 Ifthe angle of elevation from the tip of the shadow to the top of the tree is 320, what is the height of the tree to To Re nearest tenth of a degree what is the measure of angle x? he nearest tenth of a foot? us ts,can •••t Whaes the difference between problems in column A vs. Coltillkll B? In A, In 6) are muse use sides ðPftghÏ ðPriQvt A's stat ion 3: cofvnctbns Solve the following problems using your knowledge of cofunctions: eos 10 0 3. Ifsin6d= cos 9.0 then m<A is equal to: qooJ zoo 5-1 2 4. Which ',illue of-v satisfies the equation = eos(.lx sin(3x + 30 3) 12 = sin 550. lind the value of x. 5. 2K -R Csss = 80 2K +30 6. The degree measure of an ang e In a right triangle is x, and sin x = -. Which of the following equal to 2. 3 valves cos x _Ä?os (x -90) 3) cos (90-x) in(90 sink — cos( 010-Äò = L are also station L}: exact valves Set up your Reference Materials 1st! Draw the two special right triangles: 45-45-90 30-60-90 30 ***IMPORTANT!You will not be GIVENthese values on the test. You have to memorize each EXACTvalue for each angle! 2. Determine the exact trigonometric values for the follo ing: cos30 b) sin 45 4. Using exact trig values, solve for y. gntøn 5 1ŸigIdentifies s;n29 I Simplify Each Expression: 1) 1 — cos 2 0 2) tan O cos O sin sinÙ tan Ocos O sino 3) set sins ) hic-I O) station G:Avxllnrg Lines a) Given triangle DEF, ZD = 22 0, zF = 91 0, - 16.55, and EF = 6.74, find DE to the nearest hundredt 16 55 91 • 74 IIS cos(n) CBs O ßOvf\/D Ive for the area of triangle DEF. (Hint: You need the altitu e . £ - NQ-2ð h B) (nqò( A=5C 2. Given the following diagram, solve forAB to the nearest meter. (Hint: Draw altitude extending rot S)hl)-- iso bowsAl = x C, qî,gsù31Ä = x H 01 station Jumbled Jamboree 1. As shown in the diagram below, a ship is heading directly toward a lighthouse whose beacon is 125 feet short above sea level. At the first sighting, point A, the angle of elevation from the ship to the light was 70. A Ab time later, at point D, the angle of elevation was 160. 70 160 125 ft c tanlG --HBSAÀOSS 2. The water tower in the picture below is modeled by the two-dimensional figure beside it. The water tower is composed of a hemisphere, a cylinder, and a cone. Let C' be the center of the hemisphere and let D be the center of the base of the cone. 25 c: 8.5 If AC—8.5 feet, BF = 25 feet, and mLEFD = 470, determine the height of the water tower (from A to E) to the nearest whole number.