#11 GEOMETRY SECTION 7.7 NOTES and WORKSHEET Trigonometric Applications and Chapter Three Review Name________________________ Date_______Class Period_______ Target Goal: Solve application problems using Trig. ____Great ____ OK ____ Opener: Work with your group to answer #s 1‐11. 1 and 2 Set up a trig equation then solve for the variable. Round to the nearest hundredth. Circle the equation and the final solution. 1. A 2. A C 13 9 22.3 x 230 C B B y 3‐5 Determine whether you would use sin or sin‐1 on your calculator to solve each of the following. 2 x 7 3. sin A 4. sin 35 5. sin10 x 3 4 6‐11 Set up an equation and solve for the variable. Round to the nearest hundredth. Circle the equation and the final solution. 6. 7. 8. 13 cm θ 22 cm θ 32 cm 25 cm θ 34 cm 34 cm 9. 10. B x 11. A 12 cm 16° x 8 cm x 38° 18 cm 55° C Notes: For each of the following: o o o o Draw and label a diagram. Set up an equation. Solve the equation. Answer the problem. (Circle the final solution.) A 3.4 foot guy wire is attached to a tree 3 feet from the ground. What is the angle that is formed between the wire and the ground (to the nearest degree)? #2 #3 #4 #1 o The sun’s ray strike the ground at a 55 angle, 21 m from the base of the tree. What is the height of the tree (to the nearest meter)? A 15 feet ladder leans against a wall at a o 52 angle with the ground. How far from the wall is the foot of the ladder (to the nearest foot)? A little boy flies his kite. The string forms an angle of elevation of 37 o and from where he stands to directly under the kite is 45 feet. How long is the kite string (to the nearest foot)? #11 7.7 Worksheet and chapter 3 Review 1-4 1) Set up an equation and solve for θ. Circle the equation and the final solution. (Round to the nearest hundredth.) 2) 3) 4) 11 cm 12 cm θ θ 11 cm θ 24 cm 15 cm 21 cm 6 cm 16 cm θ 5-8 Set up an equation and solve for x. Circle the equation and the final solution. (Round to the nearest hundredth.) 5) 6) 7) 8) x 11 cm 21 cm 9-12 50° x x 28° 8 cm 53° 41° 30 cm x Set up an equation and solve for themissinginformation. Circle the equation and the final solution. (Round to the nearest hundredth.) 9) 10) 11) 12) 23° x x 15 cm 33° 23 cm 34 cm θ 16 cm 11 cm θ 8 cm 13 and 14 #13 For each of the following: o Draw and label a diagram. o Set up an equation. o Solve the equation. o Answer the problem. (Circle the final solution.) A 10 feet ladder reaches a window that #14 An airplane spots the floating debris at an angle of depression of 15o. If the plane is at an altitude of 3,000 feet, what is the horizontal distance before they fly over the debris (to the nearest hundred feet)? is 8 feet up from the ground. What is the angle that is formed between the ladder and the wall (to the nearest degree)? REVIEW Chapter Three----Review and Pre-Test Special Angles and Congruence 1-8 Name the given angle pairs. (Alternate Interior, Alternate Exterior, Linear Pair, Vertical, Same Side Interior, Same Side Exterior, Corresponding) 1. 1 and 3 2. 2 and 3 4. 4 and 5 3. 2 and 7 5. 3 and 8 6. 4 and 8 8. 1 and 4 7. 3 and 6 3 1 2 6 5 4 7 8 9. If m2 = 124 and m4 = 3x + 1, then x = 2 3 1 4 10‐11 Find the value of the variable in each of the following. 10. 11. 18x ‐ 13° 1130 39 – 2x° 14x ‐ 81° 12. If m1 = 48 and m2 = 4x + 4. Find the value for x. 2 3 1 4 13. A and B are complementary angles, if mA = 43 then mB = 43. T or F 14. A and B are supplementary angles, if mA = 75 then mB = 105. T or F 15. 16. Find the following: a) If A and B are supplements and mA = 132, what is mB? b) If A and B are complements and mA = 76, what is mB? c) If A and B are vertical angles and mA = 125, what is mB? d) If A and B are a linear pair and mA = 2x + 8 and mB = 3x + 2, what is the value of x? e) If A and B are vertical angles and mA = 7x ‐5 and mB = 4x + 10, what is the value of x? C and D are supplementary angles. If mC = 6x ‐ 4 and mD = 4x + 9, find x, mC, and mD. 17‐19 Solve the following for the given variable(s). 17. x = ________________ 18. x = ________________ 19. x = __________ y = __________ 127° 8x + 7 8x 3x + 40 20. Solve for x. a) x = ___________ b) x = ___________ c) x = ___________ 9x ‐ 40 5x + 4 3x + 11 9x + 8 4x ‐ 12 5x + 32 d) x = ___________ f) x = ___________ e) x = ___________ 9x ‐ 11 8x ‐ 50 85 3x + 65 5x + 25 7x + 15 21. Find the value of w. 22. Solve for w and find the measure of ABC . C 11w ‐ 9° 12w + 6° A B H F D 15w ‐ 3° G 23. Solve for k and find the measure of CBE . A 24. Solve for x and find the measure of BEF . D A 30k ‐ 4° B 25k + 6° E C B 10x ‐ 16° D C E 16x ‐ 12° F F 25. Quadrilateral FHJK is congruent Quadrilateral MNPO. Complete the following congruent statements. b) NP ______ c) M ______ a) J ______ 26. Name the pieces that are congruent given ABC DEF A AB _________ C _________ FD _________ E _________ FE _________ FED ________ d) KF ______ E B C F D 27. ABC is congruent to another triangle. Provided is some information about the two triangles, AB AG and C R. From this information determine the triangle congruence statement. ABC _________ 28. G Given: QUAD ABCD QUAD AMCG Find: mDAB = ______ MC = _______ mBCD = ______ AM = _______ 12 cm M 28° C 62° A B 10 cm 13 cm 16 cm 81° D 29. GIVEN: B E & A is the E B C PROVE: BVC CDB STATEMENTS B PROVE: EAD BAC C VCB DBC & VB || DC A midpoint of CD V 30. GIVEN: D REASON STATEMENTS REASON D 31) GIVEN: AB AE & 1 A D 2 E E B D C & AD BC B AC AD A 32) GIVEN: C PROVE: D C EDA ECB PROVE: AEC ABD STATEMENTS REASON STATEMENTS REASON 33) GIVEN: CB || ED & C CA DA PROVE: BA EA STATEMENTS A 34) GIVEN: E DB bisects ∠ABC & D AB BC B B A PROVE: C D D is the midpoint of AC REASON STATEMENTS REASON 35. Given: TR bi sec ts ATG TR bi sec ts ARG Prove: GM XM Prove: RAT RGT A 36. Given: CM bi sec ts GMX and GCX G T C M X G R Statements Reasons Statements Reasons Statements Reasons 37. Given: AB BC ,AD CD Prove: BD bisects ADC B C A D
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