Question

1: A man 2metre tall stands on thesame level ground as a vertical pole,he observe that the angle of elevation of the top of the pole is 21° and the angle of depression of the foot of the pole is 6°.find the correct to the nearest metre.
A.how far the pole is from the man
B.the height of the pole.

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

A man observes 6° angle of depression which is the horizontal to the bottom.

which means, that is the height of himself from that distance. so for every 6° angle of elevation he's observing his height

So the height of the pole

= 2m + (2m for every 6° angle of elevation )

= 2m + ( 2m×21/6)

= 2m + (7m)

=9m

Now the distance of the pole can be calculated as the horizontal line from where he's standing

we can take either the angle of depression or elevation for this

from depression we have

tan6°= 2/b

=tan 30°/5 = 2/b

=1/✓3 = 2

5 b

b/✓3= 5×2

b= 10✓3 = 17.32m

from angle of elevation

tan 21° = 7/b

b = 7/tan 21°

= 7/ 0.3838

= 18.23m( the result is slightly different using calculator)

even the first one in calculator will give you 19m approx

so 17.32 m can be considered most accurate among the three.