easy a.maths question~~~

👨🏻‍🏫 學術台數學

家仁

2009-03-14 9:07 pm

AP and BQ are 2 bngs standing vertically on a horizontal plane ABC.If the height of AP is 50m. BAC=30,ABC=45 and the angle of elevation of P and Q from C are 20 and 50,find
the angle of elevation of Q from P.
ａｎｄ我想問其實點睇elevation of呢d角,我唔係好識睇

更新1:

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更新2:

答案係19.31..

回答 (1)

用戶10012

2009-03-15 2:24 am

✔ 最佳答案

50/AC = tan 20, AC = 50/tan 20.
Angle ACB = 180 - 30 - 45 = 105.
By sine rule,
BC/sin 30 = AC/sin 45 = AB/sin 105.
BC = AC sin 30/sin 45 = 50 sin 30/tan 20 sin 45.
AB = AC sin 105/sin 45 = 50 sin 105/tan 20 sin 45.
QB/BC = tan 50 , so QB = BC tan 50 = 50 sin 30 tan 50/tan 20 sin 45.
Elevation of Q from P = arctan [(QB - AP)/AB]
= arctan [(50 sin 30 tan 50/tan 20 sin 45 - 50)/(50 sin 105/tan 20 sin 45)]
=arctan [(sin 30 tan 45 - tan 20 sin 45)/sin 105]
=14.1 degree.

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