Question

a). A flagpole stands on level ground from a point on the ground 30 meters away from it’s foot. The angle of elevation of the top of the pole is 22⁰. Find the height of the pole. b). Using the answer above, find the length from the top of the pole to the point of angle of elevation?

Answer 1

Step-by-step explanation:

Let y be the height of the flag post and x be the initial distance from flag post.

Now, after travelling 6 m towards the post the distance from the base of pole is (x−6) m.

We know that tanθ=

Adjacentside

Oppositeside

=

BC

AB

In △ABC, ∠B=90

0

and ∠C=30

0

.

Here, θ=30

0

, BC=x m and AB=y m, therefore,

tanθ=

BC

AB

⇒tan30

0

=

x

y

⇒

3

1

=

x

y

(∵tan30

0

=

3

1

)

⇒x=

3

y...........(1)

Also, in △ABD, ∠B=90

0

and ∠D=45

0

.

Here, θ=45

0

, BD=(x−6) m and AB=y m, therefore,

tanθ=

BD

AB

⇒tan45

0

=

x−6

y

⇒1=

x−6

y

(∵tan45

0

=1)

⇒x−6=y

⇒x=y+6...........(2)

Comparing equations 1 and 2, we get

3

y=y+6

⇒

3

y−y=6

⇒y(

3

−1)=6

⇒y=

3

−1

6

Hence, the height of the flag post is

3

−1

6

m.