(3 題)Problem in 2 dimensions

[匿名]

2009-05-25 4:25 am

1)A boat is 240m away from a lighthouse which is 20m high.Find the angle of depression x of the boat B as seen from the top of the lighthouse .

我的:
tan x=20/240=0.083

答案=4.764

???

2)when the elevation of the sum is 55度,find the length of the shadow cast by a vertical stick 2m high on horizontal ground.

3)A parachutist is descending vertically from c to b as shown in the figure.If AB =100m,how far(x m) does the parachutist fall as the angle of elevation from A changes from 50度 to 20度.

回答 (1)

用戶10012

2009-05-25 3:02 pm

✔ 最佳答案

1.
Your answer is correct. tan x = 0.083, so x = arctan (0.083) = 4.764 degree.
2. 2/(length of shadow) = tan 55, so length of shadow = 2/tan 55 = 2/1.428 =1.4 m.
3.
Cannot see the figure. I guess it is as follow:
Height when angle is 50 degree = 100 tan 50
Height when angle is 20 degree = 100 tan 20
so change in height = 100(tan 50 - tan 20) = 100(1.192 - 0.364)
= 100x 0.828 = 82.8 m.

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