i need help with ...

[suedw]

from the window of one building a man finds the angle of elevation to the top of a second building is 47 degrees, and the angle of depression to the bottom of the same building is 58 degrees. The buildings are 60 metres apart. find the height of the second building to the nearest metre.

 

[tkhunny]

What's your plan?

Personally, I would draw a horizontal line from the window to the opposite building and label the two given angles. Then what?

 

[mmm4444bot]

Please do not post exercises without asking any questions of your own. What have you done so far? I mean, where are you stuck? Are there some words that you don't understand?

Otherwise, did you draw a picture?

A quick sketch will show two adjacent right triangles. They share a common leg (60 meters long). The sum of the other two legs is the height of the building.

If you tell us why you're stuck on this exercise, we can then help you proceed.

 

[suedw]

Sorry, I should have been more clear, and stated my own question, just not the textbook question.

I used the Law of sine, and calculated 51.74 metres. I just wasn't sure if this is the correct method.

 

[Deleted member 4993]

Sorry, I should have been more clear, and stated my own question, just not the textbook question.

I used the Law of sine, and calculated 51.74 metres. I just wasn't sure if this is the correct method.

I am not sure about the applicability of Law sines (of triangles) here.

The easiest way was proposed before - use the definition of tangent of an angle.

The total height would be:

H = 60*[tan(47°) + tan(58°)] = 160.3621943 = 160 meters

 

[mmm4444bot]

I used the Law of sine, and calculated 51.74 metres. I just wasn't sure if this is the correct method.

Hi Sue. Subhotosh showed a tangent method. If you would like us to check your work in the future, please show us what you did.

For the benefit of future readers, here is a diagram to accompany Subhotosh's equation, where H = h[sub:1finjygv]1[/sub:1finjygv] + h[sub:1finjygv]2[/sub:1finjygv]

(Click image to expand, if needed)

[attachment=0:1finjygv]bldgs.jpg[/attachment:1finjygv]