Determine building height by viewing angles

[lamamw]

You live in the building on the left in the drawing, and a friend lives in the other building. The two of you are having a discussion about the heights of the buildings, and your friend claims that his building is half again as tall as yours. To resolve the issue you climb to the roof of your building and estimate that your line of sight to the top edge of the other building makes an angle of 21° above the horizontal, while your line of sight to the base of the other building makes an angle of 52° below the horizontal.

 

[sk1105]

I think you may have missed the rest of your question; in any case, it isn't clear what you're asking.

 

[lamamw]

oh yeah

(a) Determine the ratio of the height of the taller building to the height of the shorter building.

(b) Determine whether your friend is right or wrong.

 

[lamamw]

I think you may have missed the rest of your question; in any case, it isn't clear what you're asking.

(a) Determine the ratio of the height of the taller building to the height of the shorter building.

 

[CWatters]

Do the drawing. Mark on it the height of your building.
Write an equation for the distance between the buildings in terms of the height of your building and an angle.
Write an equation for the extra height of his building in terms of the distance between them and another angle.
Solve the equations to give the extra height of his building in terms of the height of your building.
Answer the questions.
Job done.