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CHAPTER 8

Angles of Elevation and Depression

–

Ans

tan

An observer stands at

, which is at the top of a tower,

. He sees a

car on the road at

, which is 60m from

. The angle of depression of

from

25 . Calculate the height of the tower.

A traffic light is located at

, where

CDB

is a straight

line. The angle of elevation of

from

40 .

Calculate the distance

OPERATION

. Calculate the height of the tower using

tan

The height of the tower is approximately 27.98m.

. To find the distance

, first determine

using

tan

Therefore,

is approximately 33.34m.

. The distance of

−

Hence, the distance

is approximately 26.66m.

Example 1

60Xtan 25

27.97845949

Ans

tan 40

33.34342961

–

Ans

26.65657039

60m

25°

Содержание fx-350MS

Страница 1: ...understood the usage of your CASIO fx 350MS scientific calculator may it serve you more efficiently Nellie Gan Hong Suan obtained her Bachelor degree Mathematics Economics from Universiti Malaya and her Master degree Management Science from Universiti Utara Malaysia She has seventeen years experience of teaching Mathematics She has also been involved in writing workbooks and reference books for se...

Страница 2: ...at users may extend the use of fx 350MS to learn mathematics beyond the conventional paper pen practice situation Extension of some worked examples and short cuts on using the fx 350MS to perform calculations are included within these pages Appendix 1 is a list of English Bahasa Malaysia mathematical terms used throughout the booklet Using this booklet Suppose you have no prior knowledge of using ...

Страница 3: ...adratic Functions 12 Circular Measure 13 Exploration and Investigation 1 14 Permutations and Combinations 15 Elementary Statistics 16 Exploration and Investigation 2 18 Solutions of Triangles 19 Angles of Elevation and Depression 21 Quick Check 2 23 Exploration and Investigation 3 24 Appendix 1 25 ...

Страница 4: ...3 4 5 2 expressing your answer in fraction form OPERATION 1 First choose COMP mode 2 Now key in the expression When the calculator hangs with an ERROR message press either or Express the answer in Example 1 in decimal form and improper fraction form OPERATION 1 Immediately after operations 1 and 2 in Example 1 press 2 Now try pressing these keys Right after Example 2 try pressing followed by the R...

Страница 5: ...econds Pressing or when an ERROR message is displayed will position the cursor at the location where the error occurred Calculate 5 6 3 2 2 and 5 6 3 2 2 OPERATION 1 First enter COMP mode 2 To calculate 5 6 3 2 2 press 3 Using the INS function to insert the parentheses press Press numerous times until the cursor is below then press Hence 2 16 5 6 3 2 2 and 9 5 6 3 2 2 Example 3 8 345 8 20 42 D 0 E...

Страница 6: ... decimal places press the following keys Choose 4 to specify the number of decimal places So the required answer is 59 4659 To return to normal mode Norm press Evaluate 4 5 3 π OPERATION 1 Key in the expression for evaluation Make sure the calculator is in COMP mode Note that we can omit the bracket in performing this calculation Evaluate 4 2 51 1 π and express the answer correct to 5 significant ...

Страница 7: ...es choose 5 to specify the number of significant figures Note that this is not the final answer Since the power of the 10 after 3 4169 is 1 we move the decimal point one place to the right to obtain the required answer i e 34 169cm Calculate 6 1 5 1 1 4 1 and store this value into variable A OPERATION 1 While in COMP mode press 2 To store the value into A simply press Try to think of other ways to...

Страница 8: ...ted price is 3 To calculate the price after a 28 increase press Therefore the increased price is RM305 92 Show that 15 log 27 log is equal to 15 27 log OPERATION 1 First calculate 15 log 27 log while calculator is in COMP mode 2 Now calculate 405 log since 405 15 27 Comparing the two results it is therefore shown that 15 27 log 15 log 27 log Verify that 7 15 is equal to 7 15 Also verify that 3 5 5...

Страница 9: ...pproximately 53 96 Whenever is pressed when performing calculations the calculated value is stored into Answer Memory Calculate tan 218 and rad 7 2 sin OPERATION 1 While your calculator is in COMP Deg degree mode press 2 To calculate rad 7 2 sin press Hence 218 tan and rad 7 2 sin are approximately 0 78 and 0 43 respectively Example 12 tan 218 0 781285626 sin 2 7r 0 42737988 À3 1 732050808 10Ans 5...

Страница 10: ...1 2 to its degree equivalent OPERATION 1 First enter Rad mode then perform the conversion Hence 5 78 is approximately 1 37 radian 2 Return to Deg mode and perform the conversion Hence rad 1 2 is approximately 32 120 Show that 6 π radian and 2 3π radian are equivalent to 30 and 270 respectively Example 13 78 5 1 370083463 D 0 2 1r 120 321137 R 0 ...

Страница 11: ... determine α the basic angle 3 Press once and thus obtaining the basic angle α as approximately 40 67 4 To determine the second angle which lies in the fourth quadrant press Therefore the solutions are 40 67 and 20 292 approximately Using similar operations as in Example 14 find all angles between 0 and 360 inclusive which satisfy the equation 53 0 cos x cos 1 0 38 67 66631734 Example 14 D 0 cos 1...

Страница 12: ...2 2 x x y 3 Then determine the value of y when 2 x Press followed by This means 2 y when 2 x 4 And to determine value of y when 1 x press followed by This means 5 y when 1 x 5 Use similar operations as in step 3 to find the values of y when 3 2 1 0 x The values obtained are 23 10 1 4 y respectively Hence we can construct a table of the function 4 3 2 2 x x y for 3 3 x x 3 2 1 0 1 2 3 y 5 2 5 4 1 1...

Страница 13: ... value of x for which 878 2 log x 5 What is the value of x given that 7 e x 6 Perform the following A 5 B 3 C 4 D 5 3 E π Then evaluate E C D B A 5 2 7 Express a 68 112 b 45 245 c 5 1 2 3 650 in radian 8 Express a rad 11 3 b rad 3 7 c rad 9 2 in degree 9 Which is greater 1 0 cos or 1 0 cos rad 10 Evaluate π 12 log 4 2 3 x A B y where 7 A 3 1 B and 97 2 x To check answers please see page 20 of this...

Страница 14: ... and its radius is 3cm Find the amount of material needed to produce this can OPERATION 1 First enter COMP mode 2 Calculate the area of the can using cylindrical formula jt j π π 2 2 2 Therefore the amount of material needed to produce this can is 278 97cm2 Find the volume of the can in the example given above Example 1 D 0 2ÊX32 2ÊX3X11 8 278 9734276 11 8cm 3cm ...

Страница 15: ...ne the second root we use the REPLAY function Press once to return to this display screen on right Press numerous times until the cursor is below the sign Now press Followed by the key strokes The second root is 2 5 3 To find the axis of symmetry press The axis of symmetry is 75 2 x You may scroll through the last nine calculations by pressing the Replay function Example 1 11 À 11 2 4X2X15 12 Ans ...

Страница 16: ...te the area of sector using the formula θ 2 2 1 r and store the calculated result 3 Now calculate the area of the triangle AOB using the formula θ sin 2 1 2 r 4 The area of the shaded region is Therefore the area of shaded region is approximately 0 3623cm2 ignoring the negative sign Show that the length of arc AB in the above example is approximately 2 0944cm Press to clear the memory stored in M ...

Страница 17: ...on the right Your displayed result may be different 3 Continue pressing Notice that for each press of the displayed output will change 4 To simulate 5 throws five times first key in the formula 1 6Ran and press Suppose you get the display on the right By taking the unit digit i e 5 the first throw is 5 Next we press Key Press Display Number generated Second throw 6Ran 1 3 832 3 Third throw 6Ran 1 ...

Страница 18: ...1 To determine This means that there are 3 575 880 ways to form the committee A group of five students is to be chosen from a class of 30 for a debate In how many ways can such a group be formed OPERATION 1 To form a combination of any five students from 30 students press This means that the number of combination is 142 506 Pressing will erase all memory and return the calculator to its default mo...

Страница 19: ...9 11 60 64 22 65 69 29 70 74 12 75 79 16 OPERATION 1 First determine the mid point for all class intervals Then 2 Use similar operations as in step 1 to find the rest of the mid points we will get the result as below 3 Now enter SD standard deviation mode Press 4 Input all data obtained in step 2 Weight kg Mid point Frequency 50 54 52 10 55 59 57 11 60 64 62 22 65 69 67 29 70 74 72 12 75 79 77 16 ...

Страница 20: ... 7 SHIFT 1 MODE 2 5 An estimate of the mean is 6 To find the standard deviation of weight press To input multiple entries of the same data use For example pressing input the data 3 five times Press to clear all statistics memory before performing the next statistical calculation x 65 5 ËÁn 7 466592262 n SD D 43 n SD D 72 n SD D 84 n SD D 100 ...

Страница 21: ...reen may look different Why 2 Now press followed by pressing the replay key once to return to the previous screen as shown on right Remember your display screen may look different 3 Press once We will get the display as shown on right 4 Continue on with Then and Finally Therefore we have generated the following sequence of numbers 6 15 30 51 78 Try and design another way to generate the above sequ...

Страница 22: ...o FGE is equal to 38 2 To determine y cos press Hence y cos is approximately 0 788 PQR is a triangle in which 55 PQR 63 QPR and PR 7 5cm Find the length of QR OPERATION 1 Use the formula 55 sin 5 7 63 sin QR to determine QR While in COMP Deg mode press Hence the length of QR is approximately 8 16cm Example 2 7 5Xsin 63 sin 55 8 157885924 63 55 7 5cm P Q R F E H G 104 y Example 1 180 104 2 38 180 A...

Страница 23: ... to Quick Check 1 1 a 381 078125 b 5 42 c 210 034 1658 2 a 0 034899496 b 1 c 2 3 a 7 079 457844 b 2 724069927 c 21 10019602 0 368267893 4 755 0922277 5 1 096 633158 6 12 05796327 7 a 1 966637001 b 4 289146637 c 11 35402128 8 a 178 11 23 5 b 133 41 24 5 c 166 9 27 94 9 1 0 cos 10 5 595526906 Answers to Quick Check 2 1 a 43 758 b 55 440 c 362 880 2 5 10 13 3 a 1 951 b 65 03333333 c 19 78633086 4 0 2...

Страница 24: ...located at D where CDB is a straight line The angle of elevation of A from D is 40 Calculate the distance BD OPERATION 1 Calculate the height of the tower using 25 tan 60 AC The height of the tower is approximately 27 98m 2 To find the distance BD first determine CD using CD AC 40 tan Therefore CD is approximately 33 34m 3 The distance of CD BC BD Hence the distance BD is approximately 26 66m Exam...

Страница 25: ... Calculate the distance YW c Calculate the angle of elevation of X from W OPERATION 1 Find the angle of elevation by using 257 52 tan XNY Make sure your calculator is in COMP Deg mode The angle of elevation of X from N is approximately 11 44 2 Use the formula 50 sin 257 40 sin YW to find the distance YW YW is approximately 215 65m 3 Perform this calculation right after step 2 Using YW XWY 52 tan p...

Страница 26: ... c standard deviation 4 AOB is a sector of a circle with centre at O and radius 5 2cm Given that AOB 7 π find the area of the shaded region 5 In how many ways can 12 students sit in 5 chairs arranged in a row 6 A golf club has 32 members which includes 5 doctors 4 lawyers and 3 engineers In how many ways can a committee of 5 be chosen if it is to contain one of each of these professions 7 ABC is a...

Страница 27: ...n the right This value is stored in the variable A 3 Player 2 presses until the cursor is below to delete A followed by keying in Press and to view and compare these values The person who has the greater value wins this round You may continue playing more rounds Display Player 1 Ran 1 A 5 952380952 Player 2 Ran 1 B 7 874015748 The value stores in B is clearly greater than value stores in A Hence p...

Страница 28: ...ungan Decimal Perpuluhan Distribution Taburan Equation Persamaan Estimate Anggar Expression Ungkapan Fraction Pecahan Improper fraction Pecahan tak wajar Isosceles Triangle Segitiga kaki sama Mean Min Permutations Pilihatur Power Kuasa eksponen Probability Kebarangkalian Quadrant Sukuan Random number Nombor rawak Right angled Triangle Segitiga sudut tegak Roots Punca punca Sequence Jujukan Signifi...

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