標題:
f.4 maths trigonometry
發問:
1.A balloon B is observed simultaneously from two points P and Q on a horizontal Ground. P is at a distance of c meters due north of Q. R is the projection of B on the ground . The bearings f the balloon from P and Q are Sα°E and Nβ°E respectively. The angle of elevation of B from P is θ°.(a)If the height of the... 顯示更多 1.A balloon B is observed simultaneously from two points P and Q on a horizontal Ground. P is at a distance of c meters due north of Q. R is the projection of B on the ground . The bearings f the balloon from P and Q are Sα°E and Nβ°E respectively. The angle of elevation of B from P is θ°. (a)If the height of the balloon is h metres, show that h=(c*tanθ°*sinβ°)/〔sin(α°+β°0〕
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(a) ∠PRQ=180-α-β PQ/sin∠PRQ=PR/sinβ PR =PQsinβ/sin∠PRQ =csinβ/sin(α+β) BR/PR=tanθ BR =PRtanθ =ctanθsinβ/sin(α+β) h=ctanθsinβ/sin(α+β) (b) (i) sub θ=40, α=54 and β=46 h =ctanθsinβ/sin(α+β) =100tan40sin46/sin(1 00) =61.29 h/c =61.29/100 =0.6129 (ii) QR/sinα=c/sin(α+β) QR=csinα/sin(α+β) QR=100sin54/sin100=8 2.1497 tan(the angle of elevation of B from Q)=BR/QR tan(the angle of elevation of B from Q)=61.29/82.1497=0.7 46 the angle of elevation of B from Q=36.7 (iii) PR/sinβ=c/sin(α+β) PR=csinβ/sin(α+β) PR=100sin46/sin100=7 3.0437 MR^2=PM^2+PR^2-2(PM)(PR)cosα MR=59.5145 BR=61.29 tan(the angle of elevation of B from Q)=BR/MR tan(the angle of elevation of B from Q)=61.29/59.5145=1.0 298 the angle of elevation of B from M=45.8 PR/sin∠PRQ=MR/sinα 73.0437/sin∠PRQ=59.5145/sin54 sin∠PRQ=0.9929 ∠PRQ=83.18 So the bearing of B from M is N83.18E
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