5 Trigonometry I WORkED ExAMPlE 2 Clculte the length, correct to 1 deciml plce, of the unmrked side of the tringle t right. 8 cm 14 cm On Clcultor pge, to solve equtions press: MENU 3: Alger 3 1: Solve 1. On Clcultor pge, complete the entry line s: ( 2 2 2 ) solve c = +, = 8 nd c = 14 nd > 0 To sustitute vlues use the symol ñ. Press the ctrl key / nd then = to ring up the plette. Use the Touchpd to select the ñ symol, nd then type nd or find it in the ctlog k. Complete s shown, nd then press ENTER. Press CTRL / ENTER to get deciml pproximtion. The length of the unmrked side is = 2 33 = 11.5 cm to 1 deciml plce.
WORkED ExAMPlE 7 Clculte the vlue of ech of the following, correct to 4 deciml plces, using clcultor. cos 65è57Å tn 56è45Å30ë WRITE 1 To ensure your clcultor is set to degree nd pproximte mode, press: HOME c 5: Settings 5 2: Settings 2 1: Generl 1. In the Disply Digits, select Fix 4. T to Angle nd select Degree; t to Clcultion Mode nd select Approximte. T to OK nd press ENTER. 2 On Clcultor pge, press TRIG µ to ccess nd select the pproprite trigonometric rtio. Then press: CATALOG k 5: 5 nd choose the templte for degrees, minutes nd seconds s shown. 3 Complete the entry lines s: cos 65 57 tn 56 45 30 Press ENTER fter ech entry. Since the Clcultion Mode is set to Approximte nd Fix 4, the nswers re shown correct to four deciml plces. cos 65 57 = 0.4075 tn 56 45 30 = 1.5257 32 Mths Quest 10 for the Austrlin Curriculum
WORkED ExAMPlE 9 Clculte the vlue of q : correct to the nerest minute, given tht cos q = 0.2547 correct to the nerest second, given tht tn q = 2.364. WRITE On Clcultor pge, press TRIG µ to ccess nd select the pproprite trigonometric rtio, in this cse cos -1. Complete the entry line s: cos 1 ( 0.2547) To convert the deciml degree into degrees, minutes nd seconds, press: CATALOG k 1: 1 d: D Scroll nd select DMS. Complete the entry line s: tn 1 ( 2.364) Convert to degrees, minutes nd seconds s ove. cos 1 ( 0.2547) = 75 15 rounding to the nerest minute. tn 1 ( 2.364) = 64 4 16 rounding to the nerest second. Chpter 5 Trigonometry I 33
WORkED ExAMPlE 13 Find the vlue of the pronumerl in the tringle shown. Give the nswer correct to 2 deciml plces. 5è P 120 m Ensure your clcultor is set to degree mode. On Clcultor pge, complete the entry lines s: 120 solve tn ( 5 )=, p p Then press ENTER. P = 1371.61 m correct to 2 deciml plces. 34 Mths Quest 10 for the Austrlin Curriculum
WORkED ExAMPlE 15 Find the size of ngle q in ech of the tringles shown elow. 3.1 m q 7.2 m 55 cm q 42 cm (Answer correct to the nerest minute.) On Clcultor pge, complete the entry line s: 1 7.2 tn 3.1 Then convert the deciml degrees to degrees nd minutes s descried in Worked Exmple 9. Then press ENTER. (Answer correct to the nerest second.) On Clcultor pge, complete the entry line s: 42 cos 1 55 Then convert the deciml degrees to degrees nd minutes s descried erlier. Then press ENTER. θ = 66 42 correct to the nerest minute. θ = 40 12 51 correct to the nerest second. Chpter 5 Trigonometry I 35
WORkED ExAMPlE 19 A ldder of length 3 m mkes n ngle of 32è with the wll. How fr is the foot of the ldder from the wll? How fr up the wll does the ldder rech? c Wht ngle does the ldder mke with the ground? Sketch digrm nd lel the sides of the right-ngled tringle with respect to the given ngle. H 3 m 32è y (wll) A x O On Clcultor pge, complete the entry lines s: x solve sin 32 x 3, = y solve cos( 32) y 3, = 180 ( 90 + 32) Press ENTER fter ech entry. x = 1.59 m correct to 2 deciml plces. y = 2.54 m correct to 2 deciml plces. α = 58 36 Mths Quest 10 for the Austrlin Curriculum