# Problem Solving

## Transcription

Problem Solving

Name ________________________________________ Date __________________ Class__________________ LESSON 8-3 Problem Solving Solving Right Triangles 1. A road has a grade of 28.4%. This means that the road rises 28.4 ft over a horizontal distance of 100 ft. What angle does the hill make with a horizontal line? Round to the nearest degree. _________________________________________ 2. Pet ramps for loading larger dogs into vehicles usually have slopes 2 1 between and . What is the range of 5 2 angle measures that most pet ramps make with a horizontal line? Round to the nearest degree. ______________________________________ Use the side view of a water slide for Exercises 3 and 4. The ladder, represented by AB , is 17 feet long. 3. What is the measure of angle A, the angle that the ladder makes with a horizontal line? _______________________________________ 4. What is BC, the length of the slide? Round to the nearest tenth of a foot. _______________________________________ Choose the best answer. 6. The coordinates of the vertices of RST are R(3, 3), S(8, 3), and T(8, −6). What is the measures of angle T? Round to the nearest degree. 5. Janelle sets her treadmill grade to 6%. What is the angle that the treadmill surface makes with a horizontal line? Round to the nearest degree. A 3° C 12° B 4° D 31° C ∠3 B ∠2 D ∠4 H 61° G 29° J 65° 8. Find the measure of the acute angle 3 formed by the graph of y = x and the 4 x-axis. Round to the nearest degree. 7. If cos A = 0.28, which angle in the triangles below is ∠A? A ∠1 F 18° F 37° H 49° G 41° J 53° Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. 8-25 Holt Geometry United States means a rise in elevation of 20 feet over 100 horizontal feet. A 20% grade elsewhere means a rise in elevation of 20 meters over 100 meters. 20 ft 20 m But a grade is a ratio: = . 100 ft 100 m The units cancel out, and either way a 1 20% grade simplifies to , or an angle 5 with the horizontal that measures about 11°. 6. cos R = 2 ; tan R = 1; m∠R = 45° 2 7. sin K = 3 1 ; cos K = ; m∠K = 60° 2 2 Problem Solving 6. EG = 0.61 m; FG = 0.54 m; m∠E = 57° 1. 16° 2. 22° to 27° 3. 64° 4. 34.9 ft 5. A 6. G 7. D 8. F Reading Strategies 7. KM = 56.13 mm; m∠K = 61°; m∠L = 34° 10. IJ = 5.32 yd; m∠H = 90°; m∠I = 62° 1. finding the measures of all unknown sides and angles of the triangle 9 2. m∠B = tan−1 4 11. RS = 18.98 mm; ST = 20.07 mm; m∠R = 60° 3. sin 24° = 8. BC = 3.74 ft; m∠B = 83°; m∠D = 48° 9. TV = 8.43 in.; UV = 14.08 in.; m∠T = 79° Reteach 1. ∠2 2. ∠2 3. ∠1 4. ∠2 5. 53° 6. 79° 7. 74° 8. 12° 4 AB LESSON 8-4 Practice A 1. horizontal; above 2. depression; below 9. AB ≈ 12.52 ft; AC ≈ 7.54 ft; m∠B = 37° 3. angle of depression 10. FH ≈ 9.12 mi; m∠F ≈ 26°; m∠H ≈ 64° 4. angle of elevation 11. QR ≈ 20.76 km; QS ≈ 25.04 km; m∠Q = 34° 5. angle of depression 12. WX ≈ 18.30 cm; m∠X ≈ 59°; m∠Y ≈ 31° 6. angle of elevation 13. MP = MN = 6; PN ≈ 8.49; m∠M = 90°; m∠P = 45°; m∠N = 45° 9. 11.9 meters 7. 28 feet 14. KL = 7; LJ = 3; JK ≈ 7.62; m∠L = 90°; m∠J ≈ 67°; m∠K ≈ 23° 10. 1.9 meters 1. angle of elevation 2. angle of depression 4 2. 3 3. angle of depression 4. angle of elevation 3. 53.1° 5 2 5 4. sin E = ; cos E = ; m∠E ≈ 26.6° 5 5 5. sin M = 8. 35 feet Practice B Challenge 3 1. 5 4. 67°; 23°; 12 5. 34 ft 2 in. 6. 37 ft 1 in. 7. 31 ft 10 in. 8. 1.8 m 9. 65° 3 1 ; m∠M = 30° ; tan M = 3 2 10. Mr. Shea lives above Lindsey. Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor. A12 Holt Geometry