SOLUTION: Hi! I am having trouble with this question. please help me! 40 ft. radio antenna located on top of the building. 260 ft. from the building, the angle between the bottom of the a

Question 237560: Hi! I am having trouble with this question. please help me!
40 ft. radio antenna located on top of the building. 260 ft. from the building, the angle between the bottom of the antenna and the top is 13 deg. Find the height of the building.
I would appreciate it a lot if you will include diagrams for this.
Thanks a lot!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
As far as I can tell, you should be having trouble with this problem because it doesn't make any sense.

If I understand this correctly, 260 feet away from the building, the angle between the bottom of the antenna and the top of the antenna is equal to 13 degrees.

In order for that to happen, you would have to be measuring from the top of the building 260 feet away from the building.

How would that even be possible?

If you are measuring from the ground level, then it makes more sense.

assuming you are 260 feet from the building and measuring from the ground level, then I think the problem can be solved as follows:

tan(13) = opposite / adjacent = x / 260

multiply both sides of this equation by 260 to get:

260 * tan(13) = opposite

that gets you:

opposite = 60.02572969 feet

Since opposite equals the height of the building plus the height of the antenna, this means that the building is 20.02572969 feet.

It's a short building, but the problem can be solved this way.

If you assume you are measuring from the bottom of the antenna and you are 260 feet away and the angle between the base of the antenna and the top of the antenna measured from that point is 13 degrees, then you can't possibly be 260 feet away because the same formula will compute that distance as:

tan(13) = opposite/adjacent = 40/adjacent

this means that adjacent = 40 / tan(13) = 173 feet.

since 173 feet is the distance from the bottom of the antenna to the measuring point, the distance can't be 260 feet and have the angle be 13 degrees.

A picture of what I am talking about is shown here.

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