F3 Maths....urgent---20 marks

2009-05-01 7:06 pm

1.The angle of inclination of a road is 8°. Find the rise of a car which travels a distance of 5 km horizontally.
2. A car travels 5km up a hillside with an inclination of 6° and then travels 6 km up another hillside of gradient 1 in 5. Find the rise of the car.
3.A boy walks 56m from the base of a vertical monument and finds that the angle of elevation of its top is 23°. How high is the monument? He continues to walk for a further distance from the monument in the same course until he reaches a point from which the angle of elevation from the top is 18.7°. How far is he now from where he started?
4.From a point on the ground, the angle of elevation of the top of a building is 34°. From another point 85m nearer to the building, the angle of elevation from the top is 52°. Find the height of the building.
5. From a point 26m above the ground, the angle of depression of the foot of a building is 65.2°, and the angle of elevation of the top of the tower is 34.8°. Find the height of the building.

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回答 (1)

STEVIE-G™

2009-05-01 8:04 pm

✔ 最佳答案

1)
the rise/5=tan8
the rise=0.703km
2)
the first rise=5sin6=0.523
gradient 1 in 5=> tan(inclination)=1/5=>inclination=11.3
the second rise=6sin11.3=1.18
The total rise=0.523+1.18=1.70km
3)
the height/56=tan23
the height=23.8m
Assume the final position is x m far from the starting point
the height/x=tan18.7
x=70.2
4)
Let the height be h m , the first position far from the building be x m
h/x=tan34-->x=h/tan34---(1)
h/(x-85)=tan52---(2)
Sub (1) into (2) ,
h/[(h/tan34)-85]=tan52
h=(h/tan34)*tan52-85tan52
h=12
5)
the horizontal distance between the man and the building
=26/tan65.2
=12.0m
the height/12.0=tan34.8
the height=8.34m

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