Chapter 31 Pythagoras theorem and trigonometry (2)

Transcription

1 HPTR The lengths of the two shortest sides of right-ngled tringle re m nd ( 3) m respetively. The length of the hypotenuse is 15 m. Show tht Solve the eqution Write down the lengths of the two shortest sides of the tringle. 4 The height of tringle is 4 m more thn the se. The re of the tringle is 16 m 2. Let m e the se of the tringle. Show tht ( 4) 32 Solve the eqution ( 4) 32 ind the height of the tringle. 5 The sum of the squres of 3 onseutive numers is 50. Let e the smllest of the numers. Show tht Solve the eqution. 6 The digrm 3 m shows hegon. ll the ngles re right ngles. 8 m The re of the hegon is 59 m 2. 2 m Show tht Solve the eqution Write down the length of the longest side of the hegon. 7 The digrm shows 8 trpezium. ll the mesurements re in m. The re of the trpezium is 112 m 2 4. Show tht Solve the eqution Write down the length of the longest side of the trpezium. m 8 The verge speed of r on journey of 240 km is kilometres per hour. The verge speed of the r on the return journey is 20 kilometres per hour fster. The totl time for the journeys there nd k is 10 hours. plin why Show tht Solve the eqution nd find the verge speed of the r on the return journey. hpter 31 Pythgors theorem nd trigonometry (2) erise 31 Where neessry, give lengths orret to 3 signifint figures nd ngles orret to one deiml ple. 1 The digrm shows uoid.,,,, nd re si verties of the uoid. 12 m, 15 m, 5m lulte the length of i, ii, iii. lulte the size of i ngle, ii ngle, iii ngle. 2 is tringulr prism. The retngulr plne is horizontl nd the retngulr plne is vertil. 4 m, 8 m, 10 m. 4 m 8 m 12 m 10 m lulte the length of i, ii, iii. 15 m 5 m

2 HPTR 31 lulte the size of i ngle, ii ngle, iii ngle. 3 The digrm shows pyrmid. The se,, is horizontl squre of side 10 m. The verte,, is vertilly ove the midpoint, M, of the se. M 12 m. 60 m lulte the size of the ngle tht the line mkes with the plne. Give your nswer orret to 1 deiml ple. (1387 My 2004) m lulte the size of ngle M. (4400 Novemer 2005) erise 31 1 The digrm represents uoid GH. 5 m, 7 m, 3 m. 3 m 10 m M 10 m 5 m 7 m lulte the length of G. Give your nswer orret to 3 signifint lulte the size of the ngle etween G nd the fe. Give your nswer orret to 1 deiml ple. (1387 Novemer 2004) 2 The digrm represents prism. is retngle. is squre. nd re perpendiulr to plne. 60 m. 60 m. ngle 90. ngle 30 H G 3 The digrm shows squre-sed pyrmid. The lengths of the sides of the squre se,, re 12 m nd the se is on horizontl plne. The entre of the se is M nd the verte of the pyrmid is so tht M is vertil nd M 18 m. The midpoint of is N. 12 m 18 m M lulte the length of i M, ii, iii N. Give eh nswer orret to 3 signifint lulte the size of the ngle i etween nd the plne, ii etween N nd the plne. Give eh nswer orret to 1 deiml ple. erise 31 1 Use lultor to find the vlue, orret to 3 deiml ples if neessry, of sin 150 os 110 tn 137 d os 317 e tn 244 f sin g os N 87

3 HPTR 31 2 is n otuse ngle. ind the vlue of,in degrees, when sin 0.6 os 0.38 tn Here is the grph of y sin for y erise 31 1 Work out the re of eh of these tringles. Give eh nswer orret to 3 signifint 4.8 m m 7.3 m m urtely opy this grph nd ontinue the urve to show the grph of y sin for Using your grph, or otherwise, find estimtes of the solutions in the intervl of the eqution i sin 0.7 ii sin The digrm shows prt of the urve y os for y Write down the oordintes of the point i, ii, iii, iv, v. 5 Here is sketh of prt of the grph of y sin. y P Q Write down the oordintes of i P, ii Q. (1387 June 2005) 2 lulte the re of the prllelogrm. Give your nswer orret to 3 signifint 3 Here is kite. lulte the re of the kite. Give your nswer orret to 1 deiml ple. 5.8 m m 4 The re of tringle is 33.5 m 2. 7 m 9.5 m m m 3.1 m lulte the length of. Give your nswer orret to nerest m. 88

4 HPTR 31 5 PQ is setor of irle, 83 entre nd 12 m 12 m rdius 12 m. The size of ngle PQ is 83. P Q lulte the re of tringle PQ. lulte the re of setor PQ. Hene lulte the re of the segment shown unshded in the digrm. Give eh nswer, in m 2, orret to 1 deiml ple. erise 31 1 lulte the lengths of the sides mrked with letters in these tringles. Give eh nswer orret to 3 signifint 12 m lulte the size of eh of the ute ngles mrked with letter. Give eh nswer orret to 1 deiml ple. 5 m 9.4 m m d 51 7 m m. ngle 123. ngle 35. lulte the length of. Give your nswer orret to 3 signifint figures lulte the re of tringle. Give your nswer orret to 3 signifint (4400 My 2005) 4 In tringle, ngle 60, ngle 40, 12 m. P m 12 m 9.5 m Q m 40 Work out the length of. 5 The digrm shows vertil tower on horizontl ground. is stright line. The ngle of elevtion of from is 28. The ngle of elevtion of from is m m 7.5 m m 54 lulte the height of the tower. Give your nswer orret to 3 signifint (1387 June 2006) 89

5 HPTR 31 erise 31 1 lulte the lengths of the sides mrked with letters in these tringles. Give eh nswer orret to 3 signifint 4 In tringle, 9 m, 15 m, ngle m m m 5.8 m 6.8 m m 15 m lulte the perimeter of the tringle. Give your nswer orret to the nerest m lulte the size of eh of the ngles mrked with letter. Give eh nswer orret to 1 deiml ple. 6.4 m 6 m 5 m 7.6 m 5.4 m 5.9 m erise 31G 1 frmer rrnges 90 m of fening in the form of n isoseles tringle, with two sides of length 35 m nd one side of length 20 m. 35 m 35 m 7 m 20 m m m 7.6 m lulte the re enlosed y the fening. Give your nswer orret to 3 signifint Lter the frmer moves the fening so tht it forms different tringle,. 20 m 40 m 30 m 6 m 10 m 20 m 30 m lulte the length of. Give your nswer, in entimetres, orret to 3 signifint lulte the size of ngle. Give your nswer orret to 3 signifint (1385 June 2001) 40 m lulte the size of ngle. Give your nswer orret to 1 deiml ple. (4400 My 2006) 90

6 HPTR m. 8.4 m The re of tringle is 10 m 2. lulte the perimeter of tringle. Give your nswer orret to 3 signifint (1387 June 2004) 3 stright rod UW hs een onstruted to y-pss villge. The originl stright rods U nd W re 4 km nd 5 km in length respetively. lies on ering of 052 from U. W lies on ering of 078 from. The verge speed on the route UW through the villge is 30 kilometres per hour. The verge speed on the y-pss route UW is 65 kilometres per hour. U lulte the time sved y using the ypss route U. Give your nswer to the nerest minute. (1384 June 1995) 4 The digrm shows shows pyrmid. The pe of the pyrmid is. h of the sloping edges is of length 6 m. The se of the pyrmid is regulr hegon with sides of length 2 m. is the entre of the se. N 52 2 m 4 km 6 m 6 m N 2 m m 5 km 2 m 8.4 m W 2 m lulte the height of ove the se of the pyrmid. Give your nswer orret to 3 signifint lulte the size of ngle. Give your nswer orret to 3 signifint lulte the size of ngle. Give your nswer orret to 3 signifint (1387 June 2005) hpter 32 Simultneous liner nd qudrti equtions erise 32 1 Solve these simultneous equtions. y 3 nd y 2 y 4 nd y 2 2 y 3 nd y 2 1 d y 5 nd y 2 5 e y 8 nd y 2 f y 2 nd y Solve. y 4 nd y 2 2 y 2 3 nd y 2 3 y 3 1 nd y 2 3 d y 4 nd y e y 4 nd y 2 4 f y 3 4 nd y g 2 y 1 nd y 2 2 h 2y 1 nd y i 4 3y 10 nd y j 2 3y 4 nd y