Year 9 Trigonometry 4 - Dobmaths

1 Year 9 Mathematics Trigonometry Practice Test 4. Name_____. 1 Label the sides of the triangle below hypotenuse, opposite and adjacent 2 Label the triangle below with opposite, hypotenuse and . MQ 9 NSW - 14 Page 495 Sunday, July 25, 2004 9:08 AM. MQ 9 NSW - 14 Page 495 Sunday, July 25, 2004 9:08 AM. Chapter 14 Right-angled Trigonometry 495. Trigonometric ratios are used to determine Cthe h a p tunknown e r 1 4 R i g hside t - a n g lengths l e d t r i g o and 495. n o m eangles try of a right-angled triangle. 3 To determine For this triangle, write which downTrigonometric the one of expressions thefor ratios three are usedtrigonometric the sine, cosine the to determine ratios and to use tangent unknown in lengths ratios side eachofcase, followof a and angles the given anglethese steps. right-angled triangle. Step 1 Label theTosidesdetermine which of the one of the triangle, threeare which trigonometric either given, ratiosor to need use in to each becase, follow found, these steps.

2 Using the symbols O, A, H with respect to the angle in question. Step 1 Label the sides of the triangle, which are either given, or need to be found, Step 2 Consider the sides which are involved and write the trigonometric ratio con- using the symbols O, A, H with respect to the angle in question. tainingStep these sides. 2 Consider (Usethe the sidesmnemonic SOH CAH TOA. which are involved and write the to trigonometric assist you.) ratio con- Step 3 Identify the values of the pronumerals in the ratio. taining these sides. (Use the mnemonic SOH CAH TOA to assist you.). Step 4 Substitute Step the values the 3 Identify of values the pronumerals into the of the pronumerals ratio. in the ratio. Step 4 Substitute the values of the pronumerals into the ratio. 4 WORKED WORKED. Example Write the trigonometric 5 5. ratio which must be used in order to find the value of the Example pronumeral in each of the following triangles.

3 Write the trigonometric ratio which mustwhich Write the trigonometric ratio be used mustinbeorder toorder used in find to thefind value of theof the the value a) pronumeral in each of the following triangles. pronumeral in each of the following b) triangles. a a b b 18 18. 15. 15 x x 6. 6 50 . 50 . b b THINK WRITE. THINK a 1 Label the sides of the triangle whose lengthsWRITE. are a given, using the appropriate symbols. a 1 Label the sides of the triangle whose lengths are a 15 = H. 6=O. given, using the appropriate symbols. he equation by multiplying x = tan 58 . uate, then round your answer x = 419 37. x m r, press 5 Evaluate each of the following giving answers correct to 4 decimal places . a) sin 56 b) cos 35 c) tan 78 . 6 Find the value of x correct to 2 decimal places xample we found the opposite side, having been given the adjacent side. g into the tangent ratio formula, the x was in the numerator and the given denominator.

4 In the next worked example the unknown side is in the 8. 7 Find the value of m correct to 2 decimal places7. ple marked m in the triangle at right. cm to 2 decimal places. 22 . m WRITE/DISPLAY. 8 Calculate each of the following correct to 2 decimal places MQ 9 NSW - 14 MQ. Page9 511. NSWS unday, JulyPage - 14 25, 511. 2004 Sunday, 9:08 AMJuly 25, 2004 9:08 AM. angle using the symbols O, a) cos 65 57' cm = A b) tan 56 45' 30 . 22 angle. 9. O. Find the size of angle ! correct to22 C h a p t e r 1 4 R iC. the nearest degree, g hh ta-patnegrl e1d4 t Rr i g o given sin ! = 511. h nt -oamn eg lt er dy t r i g o n o m e t r y 511. MQ. MQ 9 NSW - 14 Page 9 NSW. 510 Sunday, - 1425,Page 2004510 Sunday, 9:08 = H25, 2004 9:08 AM. AMm July 10 Find the value of !:". A. tenuse (H) givenTHINK. the adjacentTHINK cos = ---- WRITE/DISPLAY WRITE/DISPLAY. containing these sides. 4 Make using 510.

5 A) correct to the nearest M a t h sthe Q4. inverse usubject e sMake 510. tangent. using o H minute, given that cos ! =. M rathe t 9 fof h se equation the tN. inverse subject w e su tt hof Q uS o tangent. 9 Wf the e5w. 2 SPoautt . equation oa rl e sN hhw=W. a ytan 1 5. - ) = tan 1( ----- a l e s ( 5----- 11. 2 P a t h w a y 5. 11. -). e variables. b) correct to the = 22 , nearest A =second, cm, given H = that m tan ! = Evaluate and and to round, correct 5 Evaluate the correct to the 24 . round, 24 . WORKED WORKED 12 12. 5. Continued over page 11 For each nearest Example ofdegree. the following Example find nearest degree. the size of the angle marked with a pronumeral, correct to the nearest degree. On a Casio graphics calculator, this would Onfollowing For each of the a Casio For eachgraphics of the find calculator, thefollowing size of the this find would the angle size of the marked angle with marked withcorrect a pronumeral, a pronumeral, to correct to be as shown onbethe as screen shown atonright.

6 The screen at right. the a)nearest the degree. nearest degree. b). a a b b 5m 5m 5 cm 5 cm cm cm . When asked forWhena more accurate asked for a measurement more accurateofmeasurement an angle we ofarean11. able to use angle m the able we are calcu- to use the calcu- 11 m lator to find anlator angletocorrect to the nearest minute or nearest second. find an angle correct to the nearest minute or nearest second.. 13. THINK WRITE/DISPLAY. 13. THINK WRITE/DISPLAY. WORKED WORKED. 12 Find the sizeExample of angle to the nearest minute in each triangle below. Example a 1 ofLabel a 1 Label the sides the sides of the the triangle. a Find the size of a) Find the size angle in each of the of angle triangles in each ofshown b)below. shown below. the triangles a m a m b b H O H O. 5 cm 5 cm cm cm 55 cm 55 cm m m . A A. O . O. 2 Identifytrigonometric 2 Identify the appropriate sin = ---- 42 cm sin = ---- the appropriate trigonometric 42 cm H H.

7 Ratio to (Answer use. We correct ratio to are to use. given WeH, O and aresogiven O and H, (Answer so to correct (Answer correct to (Answer correct to choose the the nearest minute.). the choose sinenearest ratio. the sine ratio. the nearest second.). minute.) the nearest second.). 3 Substitute O = and H = 5 Oand= and H = 5 andsin = ------- sin = ------- THINK WRITE/DISPLAY 5 5. evaluateTHINK evaluate the expression. the expression. WRITE/DISPLAY. = = 13 A ladder of length 3 m makes an angle of 32 with the wall. a) How far is the foot of the ladder from the wall? "b) How far up the wall does the ladder reach?"c What angle does the ladder make with the ground? 14 From an observer, the angle of elevation of the top of a tree is 50 . If the observer is 8. metres from the tree, find the height of the tree. 15 Change each of the following compass bearings to true bearings.

8 A) N32 E b) S14 W. 16 Change each of the following true bearings to compass bearings. a 220 T b 130 T. a) 220 T b) 130 T. 17 A boat travels a distance of 5 km from A to B in a direction of 035 T. a) How far east of A is B? b) How far north of A is B? c) What is the true bearing of A from B?