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Basic Education KwaZulu-Natal Department of Education REPUBLIC OF SOUTH AFRICA NAME:........................................................................................................................... MATHEMATICS COMMON TASK - INVESTIGATION TERM 1 2019 S.B.A TASK GRADE 10 MARKS: 60 TIME: 1 hour 2 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This investigation consists of 3 questions. 2. Answer ALL the questions. 3. Number the answers correctly according to the numbering system used in this question paper. 4. Clearly show ALL calculations, diagrams, graphs et cetera that you have used in determining your answers. 5. Answers only will not necessarily be awarded full marks. 6. You may use an approved scientific calculator (non-programmable and nongraphical), unless stated otherwise. 7. If necessary, round off answers to TWO decimal places, unless stated otherwise. 8. Write neatly and legibly. 3 QUESTION 1 1.1 Solve for x in the triangle below given that AB = 4cm , BC = 3cm and AC = x. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (2) 1.2 In the diagram below, given that XY = 3cm , X Z Y 30 0 and YZ = x, is it possible to solve for x using the theorem of Pythagoras? Motivate your answer. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (2) [4] 4 QUESTION 2 In each of the similar triangles labelled 1 to 5 on your diagram sheet, the OPP (opposite), ADJ (adjacent) and HYP (hypotenuse) sides are denoted by the letters o, a and h respectively: 2.1 2.2 2.3 Measure the length of each side, and record your measurements in the columns assigned for that, to the nearest mm, in the table below. (5) Measure each of the marked angles and record your measurement in the column assigned for that, to the nearest degree, in the table below. (5) When you are done with your measurements, use them to complete the remaining columns on ratios, as indicated. (18) Lengths in mm Angle OPP (0) ADJ (a) HYP (h) Ratios Fraction Decimal (2dp) Fraction Decimal (2dp) Fraction Decimal (2dp) 1 2 3 4 5 2.4 Write down the mean values of your ratios below: (use the decimal columns to work them out): (6) opposite = hypotenuse 2.5 = = Complete the statement below by writing down your observation on the values of your respective ratios for each of the triangles 1 to 5: 2.5.1. Even though the triangles are all different sizes, the decimal values for each ratio are____________________________.” (2) 5 2.5.2. Although the sides of the triangles are of different measurements 2.5.2.1. all triangles are ……………………angled triangles . (1) 2.5.2.2. the angle opposite the OPP side is ………..……….. (1) 2.5.2.3. the corresponding sides of all these triangles are in ………...... (1) [39] QUESTION 3 These ratios (from 2.4. above) are given special names . = sine = cosine = tangent All 3 of the above ratios are written as sin Θ or cos Θ or tan Θ Where Θ is the angle of reference . For example sin 30̊ , so sin 30̊ = 3.1 Now use your calculator to evaluate the following values to 2 decimal places: sin30o cos30o tan30o (6) 3.2. Compare your values in question 3.1 with the mean values you calculated in question 2.4 and draw a conclusion from your observation. Write down your conclusion below. ___________________________________ ________________________________ ___________________________________________________________________ (3) 6 3.3. What would happen if the angle measured in table 2.3 was 42̊ ? Explain your answer by calculating any one of the three trigonometric ratios discussed above. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ __________________________________________________________________ (4) 3.4. Using the knowledge, you have discovered in this investigation, solve for x in question 1.2. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (4) 3.5 In PQR below, QR = 5,5 cm and Q R P =60o, calculate the length of PR. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ (3) [20] GRAND TOTAL: 60 Diaeram Sheet 1. ldentify sides 2. Measure the length of each side (in mm). ' 3.' Measure the marked angle 4. Record on table Provided