(3 題)Problem in 2 dimensions

Question

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.

Answer 1

Favorite Answer

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.