duckcowhybrid
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- Dec 20, 2008
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- 2010
Help guys. Much appreciated.
1. Two vertical poles height a and b subtend the same angle Y at a point P in the line joing their feet A and B . If Q is another point on the orizontal plane and AQB=90 the poles subtend angles of alpha and beta at Q.
Prove (alpha + beta)^2 cot^2 Y = a^2 cot^2 alpha + b^2 cot^2 beta.
2. The side of a hill faces south and is inclined to the horizon at an angle of a. A straight railway on the hill is inclined at an angle B.If the bearing of the railway is Y degrees east of north, show that Cos Y = cota a tan b
3. An aeroplane flies horizontally due east at a constant speed of 240 km/h. From a point P on the ground the bearing of the plant at one instant is 311T while the 3 minutes later the bearing is now 73T whilsts its elevation then is 21. If h is the altitude of the plane, show that h= sin 41 tan 21 cosec 58 and calculate h to the nearest metre.
4. A person walking on a straight road observes a tower at a a bearing of 45T at an angle of elevation of 5 degrees. After walking 5000m, the tower now bears 315T and is now at an angle of elvation of 8 degrees. Find the height of the tower and determine the angle made by the road and another road bearing 90T
Much thanks for answers to any of them (preferable Questiosn 1,2,3.) These Questions come from Set HD2 in the Coroneos Supplement for those interested.
1. Two vertical poles height a and b subtend the same angle Y at a point P in the line joing their feet A and B . If Q is another point on the orizontal plane and AQB=90 the poles subtend angles of alpha and beta at Q.
Prove (alpha + beta)^2 cot^2 Y = a^2 cot^2 alpha + b^2 cot^2 beta.
2. The side of a hill faces south and is inclined to the horizon at an angle of a. A straight railway on the hill is inclined at an angle B.If the bearing of the railway is Y degrees east of north, show that Cos Y = cota a tan b
3. An aeroplane flies horizontally due east at a constant speed of 240 km/h. From a point P on the ground the bearing of the plant at one instant is 311T while the 3 minutes later the bearing is now 73T whilsts its elevation then is 21. If h is the altitude of the plane, show that h= sin 41 tan 21 cosec 58 and calculate h to the nearest metre.
4. A person walking on a straight road observes a tower at a a bearing of 45T at an angle of elevation of 5 degrees. After walking 5000m, the tower now bears 315T and is now at an angle of elvation of 8 degrees. Find the height of the tower and determine the angle made by the road and another road bearing 90T
Much thanks for answers to any of them (preferable Questiosn 1,2,3.) These Questions come from Set HD2 in the Coroneos Supplement for those interested.