trigonometry help
Student’s name Teacher’s name _________________________________ _____________________________ 2021 Task 3: Take Home Task- Trigonometry Mathematics Standard 2 General Instructions Reading time – 5 minutes Working time – 2 Weeks Write using blue or black pen Black pen is preferred Calculators may be used A formulae sheet is provided at the back of this paper Total Marks – 30 Section I: Pages 2 to 4 9 marks Attempt questions 1-3, using the answer sheet on page. Ensure all working out has been provided Section II: Pages 5 to 7 9 marks Attempt questions 4-6. Ensure all working out has been provided Section III: Pages 8 to 11 12 marks Attempt questions 7-8 Ensure all working out has been provided Section I (9 Marks) Section II (9 Marks) Section III (12 Marks) Total (30 Marks) % Grade Student Comment: Please ensure this section has been completed upon submission. This involves strengths/ weakness/ challenges you faced during the completion of the task. Teacher Comment: Section 1 – Band 4 Questions (9 marks) 1 . The point A is 32 m from the base of a building. The angle of elevation from A to the top of the building is 42°. Show that the height of the building is approximately 28.8 m. (2 mark) _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ A car is parked 74 m from the base of the building. (2 marks) What is the angle of depression from the top of the building to the car? Give your answer to the nearest minute. _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 2. Town is 62 km due south of Town . Town is on a bearing of from and is due west of B. Find the size of (1 mark) ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Find the distance between Towns A and C, to the nearest kilometre. (2 marks) ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 3. Using the sine rule, find the value of correct to one decimal place. (2 marks) ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Section 2 – Band 5 Questions (9 marks) 4. The diagram shows a triangle with side lengths 24 cm and 52 cm and angle 27° and . (3 marks) Find , given it is an obtuse angle. Give your answer to the nearest minute. ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 5. Find the area of triangle, correct to the nearest square metre. (3 mark) ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 6. A compass radial survey of the field has been conducted from . (3 marks) Find the area of the section , to the nearest square metre. ___________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Section 3 – Band 6 Questions (12 marks) 7. A ship sails 8 km from to on a bearing of 134°. It then sails 12 km to . The size of angle is 119°. What is the bearing of from ? (2 marks) ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Find the distance . Give your answer correct to the nearest kilometre. (2 marks) ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ What is the bearing of from ? Give your answer correct to the nearest degree. (3 marks) ______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ _______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ 8. The diagram shows two triangles. Triangle is right-angled, with and is . In triangle and . The area of triangle is What is the value of , correct to one decimal place? (3 marks) __________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Find the length of to 1 decimal place. (2 marks) _________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ Rutherford Technology High School Standard 2: Task 3 12