SOLUTION: A flagpole is placed on top of a pedestal at a distance of 15m. from the observer. The height of the pedestal is 20m. If the angle subtended by the flagpole at the observer is 10 d

Algebra ->  Trigonometry-basics -> SOLUTION: A flagpole is placed on top of a pedestal at a distance of 15m. from the observer. The height of the pedestal is 20m. If the angle subtended by the flagpole at the observer is 10 d      Log On


   

Question 1205338: A flagpole is placed on top of a pedestal at a distance of 15m. from the observer. The height of the pedestal is 20m. If the angle subtended by the flagpole at the observer is 10 degree. Compute the height of the flagpole.
Found 2 solutions by KMST, ikleyn:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The fact that we are given the height of the pedestal, suggest that the height of the pedestal is relevant.
In real life, we would ask how high the eye of the observer is relative to the base of the pedestal.
Is the observer standing up? How tall is the observer?
Is the ground horizontal between the observer and the bottom of the pedestal?

I'll sketch two right triangles with the eye of the observer, the bottom and top of the pedestal, and the top of the flagpole as vertices.
Let h be the height of the flagpole in meters.

Observer lying on the grass on horizontal ground
tan%28red%28A%29%29=20%2F15 --> red%28A%29=53.13%5Eo
red%28A%2B10%5Eo%29=53.13%5Eo%2B10%5Eo=63.13%5Eo
tan%28red%28A%2B10%5Eo%29%29=tan%2863.13%5Eo%29=1.97367=%2820%2Bh%29%2F15 --> h=1.97367%2A15-20
h=highlight%289.6%29

Note: If I was the observer I would be standing up, with my eye 1.6 m above ground level.
Then, the vertical height of the top of the pedestal above the eye of the observer would be 18.4 m instead of 20 m.
As a consequence, the triangles would have been a little different, and the calculated height of the flagpole would round to only 6.9 m.

Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.

Dear tutor @MKST !

Glad to see you acting at this forum.   Come again more often !


The fact that the height of the observer is not given,  means that this height is  IRRELEVANT.

In other words, it means  (by default)  that the problem  SHOULD  BE  solved
in the simplest arrangement from the point of view of an ant crawling on the grass.