Calculate the length, correct to 1 decimal place, of the unmarked side of the triangle at right.

Transcription

1 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: ( ) 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.

2 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 tn 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 = tn = Mths Quest 10 for the Austrlin Curriculum

3 WORkED ExAMPlE 9 Clculte the vlue of q : correct to the nerest minute, given tht cos q = correct to the nerest second, given tht tn q = 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 ( ) 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 ( ) = rounding to the nerest minute. tn 1 ( 2.364) = rounding to the nerest second. Chpter 5 Trigonometry I 33

4 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 = m correct to 2 deciml plces. 34 Mths Quest 10 for the Austrlin Curriculum

5 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: 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 = correct to the nerest minute. θ = correct to the nerest second. Chpter 5 Trigonometry I 35

6 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 ( ) Press ENTER fter ech entry. x = 1.59 m correct to 2 deciml plces. y = 2.54 m correct to 2 deciml plces. α = Mths Quest 10 for the Austrlin Curriculum