Chapter 7: Right Triangles and Trigonometry Name: Study Guide Block: Section and Objectives

Transcription

1 Page 1 of 22 hapter 7: Right Triangles and Trigonometr Name: Stud Guide lock: SOL G.8 The student will solve real-world problems involving right triangles b using the Pthagorean Theorem and its converse, properties of special right triangles, and right triangle trigonometr. lock / Date Section and Objectives 7.1 ppl the Pthagorean Theorem Identif the legs and hpotenuse of a right triangle Find the length of the hpotenuse of a right triangle Find the length of a leg of a right triangle Solve word problems involving right triangles Find the area of an isosceles right triangle Memorize common Pthagorean Triples 7.2 Use the onverse of the Pthagorean Theorem lassif triangles as right, acute, or obtuse b appling the onverse of the Pthagorean Theorem 7.3 Use Similar Right Triangles Draw the three triangles that result when an altitude is drawn to the hpotenuse of a right triangle Write three similarit statements that result from the drawing of the three triangles that result when an altitude is drawn to the hpotenuse of a right triangle ppl the Geometric Mean (ltitude) Theorem ppl the Geometric Mean (Leg) Theorem 7.4 Special Right Triangles Determine the length of the hpotenuse for a triangle given a leg Determine the length of the legs for a triangle given the hpotenuse Identif the short leg, long leg, and hpotenuse in a triangle Determine the length of an missing side of a triangle given one of the sides lasswork and Homework W Pthagorean Theorem and onverse (KUT) WS Practice 7.1 & 7.2 W Using Similar Right Triangles (KUT) Quiz net class on 7.1 and 7.2 Quiz on W Special Right Triangles (KUT) WS Geometr Review WS Practice 7.4 Dan Muscarella, 2013

2 lock / Date 4 5 Section and Objectives 7.5 ppl the Tangent Ratio and 7.6 ppl the Sine and osine Ratios Identif the opposite side, adjacent side, and the hpotenuse to a given angle in a right triangle Write the sine, cosine, and tangent ratios as both a fraction and decimal ppl the sine, cosine, and tangent ratios to determine missing side lengths in a right triangle Solve problems involving the angle of depression and the angle of elevation 7.7 Solve Right Triangles Solve a right triangle Use inverse sine, inverse cosine, and inverse tangent to approimate the angle measurements in a right triangle Page 2 of 22 lasswork and Homework Quiz HW Trig (KUT) WS SohahToa WS Solving Right Triangles (KUT) EL Gizmo: Sine, osine, Tangent 6 Review STUDY!! 7 Test h 7 Post Test Reflection (online) h 8 Pre-Test (online) Dan Muscarella, 2013 Helpful Hints e sure to watch the videos for each lesson before ou come to class. ome to class with specific questions. To receive full credit for our work, ou need to include all drawings and show the work that leads to our solution. If this is missing, ou will not receive an credit. Fill out our formula sheet as we go along. There are lots of formulas in this chapter; stud them dail so ou have them memorized.

3 Page 3 of 22 hapter 7 Formula Sheet Pthagorean Theorem and the Pthagorean First: onverse of Pthagorean Theorem: Triples: S + M L Right cute Obtuse Geometric Mean Ratios for Right Triangles: Picture h Draw 3 triangles: D Proportions Similarit statement Special Right Triangles: SOH H TO: sin = cos = Wh would ou use the following? sin 1 tan =

4 Page 4 of 22 Geometr Name Date Pd Pthagorean Theorem Pthagorean Theorem E: Find the length of the unknown side of the right triangle. Determine whether the unknown side is a leg or hpotenuse foot ladder rests against the side of the house, and the base of the ladder is 4 feet awa. pproimatel how high above the ground is the top of the ladder? 6. Find the area of an isosceles triangle with side lengths 10 meters, 13 meters and 13 meters.

5 Page 5 of 22 lassifing Triangles Right, cute, Obtuse, or No Triangle First Second c 2 a 2 + b 2 c 2 a 2 + b 2 c 2 a 2 + b 2 Tell whether the given triangle is a right triangle Tell whether a triangle with the given side lengths is a right triangle. 9. 4, 4 3, , 11, and , 6, and an segments with lengths of 4.3 feet, 5.2 feet, and 6.1 feet form a triangle? If so, would the triangle be acute, right, or obtuse? 13. Show that segments with lengths 3, 4, and 6 can form a triangle and classif the triangle as acute, right, or obtuse.

6 Page 6 of 22 Geometr WS Practice 7.1 & 7.2 Name Use to determine if the equation is true or false. 1. b 2 + a 2 = c 2 2. c 2 a 2 = b 2 3. b 2 c 2 = a 2 4. c 2 = a 2 b 2 b c 5. c 2 = b 2 + a 2 6. a 2 = c 2 b 2 a Find the unknown side length. Simplif answers that are radicals Find the area of the figure. Round decimal answers to the nearest tenth ft 10 ft 4 cm 12 cm 14 in. 11 in. 20 in. Decide whether the numbers can represent the side lengths of a triangle. If the can, classif the triangle as right, acute, or obtuse , 12, ,4, , 21, 28

7 Page 7 of 22 Geometr Name 7.3 Similar Right Triangles Date Pd Theorem 7.5 If the altitude is drawn to the hpotenuse of a right triangle, then the two triangles formed are similar to the original triangle and to each other. Small Medium Large D Similarit Statement: 1. Identif the similar triangles in the diagram. Then, write a similarit statement. U S R T 2. Find the value. No decimals! R 3 S 9 Q P

8 Page 8 of Find the value of k k 4. Find the value of cross section of a group of seats at a stadium shows a drainage pipe D that leads from the seats to the inside of the stadium. What is the length of the pipe if = 20 ft, = 30 ft, and = 10 3 ft? D

9 Page 9 of 22 Geometr WS Practice 7.3 omplete and solve the proportion.? 1. = =? 9 3. =? Find the value(s) of the variable(s). 4. a b 24 z Tell whether the triangle is a right triangle

10 Page 10 of 22 Geometr Name 7.4 Special Right Triangles Date Pd Theorem Triangle Theorem hpotenuse = leg 2 leg = hpotenuse Find the length of the hpotenuse Find the lengths of the legs in the triangle Theorem Triangle Theorem hpotenuse = long leg = 2 short leg short leg 3 Short leg Hpotenuse short leg = hpotenuse 2 long leg 3 short leg = 3 3 Long leg

11 Page 11 of 22 Find the value(s) of the variable(s) The logo on a reccling bin resembles an equilateral triangle with side lengths of 6 centimeters. What is the approimate height of the logo?

12 Page 12 of 22 Geometr Review: Name: omplete all work on a separate sheet of paper. Include all drawings. heck our answers using the answer ke! Use Pthagorean Theorem!! Remember, to be a triangle: Small + Medium > Large Then, classif as R,, or O (Pthagorean Theorem!)

13 Page 13 of 22 nswer Kes Lesson 7.1 Practice Lesson 7.2 Practice Yes Yes No Right Obtuse cute Not a triangle Right Obtuse Lesson 7.3 Practice =, = = 3, = = 4, = = 8, = = 2, = z 4 =, z = 2 4 z

14 Page 14 of 22 Geometr Non-alculator Name WS Practice 7.4 Find the value of. Write our answer in simplest radical form Find the value of each variable. Write our answers in simplest radical form omplete the table b a 30 c 60

15 Page 15 of 22 Geometr Name Date Pd trigonometric ratio 3 basic trig ratios: SohahToa sin = side opposite a = hpotenuse c hpotenuse cos = side adjacent b = hpotenuse c c a side opposite tan = side opposite a = side adjacent b b side adjacent Eamples: Find the sin, cos, and tan ratios for each acute angle in the triangle. Write each answer as a fraction and as a decimal rounded to four places. S R T

16 Page 16 of 22 Find the value of (and ) You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26. Find the height and length of the base of the ramp. 7. You are skiing on a mountain with an altitude of 1200 meters. The angle of depression is 21. bout how far do ou ski down the mountain?

17 Page 17 of 22 Geometr WS Practice SohahToa Name Use the diagrams at the right to find the trigonometric ratio. 1. sin K 2. cos 3. tan 4. sin J c a j l 5. cos K 6. tan K b L k J Use a calculator to approimate the given value to four decimal places. 7. sin cos tan sin tan cos tan sin 83 Fill in the blank then solve for the variable. Round decimals to the nearest tenth. 15. sin 52 =? 16. cos? = tan 24 = 8? Find the value of each variable. Round decimals to the nearest tenth

18 Page 18 of 22 Geometr Name 7.7 Date Pd Solving Right Triangles to solve a right triangle ou must know either: - two side lengths - one side length and one acute angle Inverse Trigonometric Ratios Used to find angle measurements inverse sine - If sin =, then sin -1 = m inverse cosine - If cos =, then cos -1 = m inverse tangent - If tan = z, then tan -1 z = m Eamples: 1. Use a calculator to approimate the measure of to the nearest tenth of a degree Let and be acute angles in a right triangle. Use a calculator to approimate the measures of and to the nearest tenth of a degree. a. sin = 0.87 b. cos = 0.15

19 Page 19 of Solve the right triangle. Round decimals to the nearest tenth ft 4. Solve the right triangle. Round decimals to the nearest tenth. G 14 H 16 J

20 Page 20 of 22 hapter 7 Review Find the unknown side length. Write our answer in simplest radical form lassif the triangle formed b the side lengths as right, acute, or obtuse. 4. 4, 5, , 12, , 13, 23 Find the value of each variable. Round each answer to the nearest tenth z Find the value of the variable. Round each answer to the nearest tenth

21 Page 21 of Write a similarit statement for the three similar triangles in the diagram. Then solve for. S R 15 P 21 Q Find the area of the isosceles triangle h Use the trig ratios to find the value of. Round to the nearest tenth Find the value of each variable using special right triangles. Leave answers in simplest radical form

22 18. Find the value of F and G. 19. Find the value of and. Page 22 of 22 H 96 G F 20. Solve the right triangle. (find EVERYTHING!) Round answers to the nearest tenth. P 20 R 14 Q 21. chair lift on a ski slope has an angle of elevation of 28 and covers a total distance of 4640 feet. To the nearest foot, what is the vertical height of the chair lift?