F3 Maths 10 points

2011-08-29 7:02 pm

Need steps , thx a lot :)

1) H , a point on the x-axis, divides AB internally in the ratio r : 1.
Find
(a) the value of r;
(b) the coordinates of H
Picture: http://www.hotimg.com/image/SvwnpsG
2) Given the bearing of B from A is S30°E. If B is rotated about A by 90° clockwise, find the bearing of B from A.
3) A car is 200 m away from the foot of a tower of height 230 m . Find the angle of depression of the car from the top of the tower.

回答 (1)

胡雪8°

2011-08-29 8:14 pm

✔ 最佳答案

1)
(a)
y-coordinate of H = 0

0 = [50 + r(-30)]/(1 + r)
50 - 30r = 0
r = 5/3

(b)
Let a be the x-coordinate of H.
a = [-30 + (5/3)50]/[1 + (5/3)]
a = (160/3)/(8/3)
a = 20

Hence, the coordinates of H = (20, 0)

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2)
The new bearing of B from A
= S (90° - 30°) W
= S 60° W

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3)
Let θ be the angle of depression of the car from the top of the tower.
Then, θ is also the angle of elevation of the top of the tower from the car.

tanθ = 230/200
θ = 49.0°
The angle of depression of the car from the top of the tower = 49.0°

參考: 胡雪

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