Help with Sine Law Word Problem

[mattapus]

Hello,

I've been doing pretty well so far into my Grade 11 Trigonometry unit. We've been covering the sine law and it all made perfect sense until we were assigned some word problems for home work. Now I'm struggling. I don't think they're too difficult if you know how to go about them properly. I think I'm just missing something. I was hoping I could post one (with the final answer) and maybe someone could solve it and show the steps?

Any help would be much appreciated. Below is the problem exactly as written in my textbook. No diagram or drawing is included with the problem; you are to come up with the diagram yourself. The textbook says final answer is 299.8 m.

Problem:

The Pont du Grand near Nimes, France, is a Roman aqueduct. An observer in a hot-air balloon some distance away from the aqueduct determines that the angle of depression to each end is 54° and 71°, respectively. The closest end of the aqueduct is 270.0 m from the balloon. Calculate the length of the aqueduct to the nearest tenth of a metre.

Thanks!

[stapel_eliz]

Draw the right triangle showing a vertical line for the height "h" of the balloon above the aqueduct's horizontal, the horizontal distance "y" from the base of the vertical to the closer end of the aqueduct, and the slanty line labelled "270" showing the line-of-sight distance. Label the given angle and the right angle.

Solve this triangle.

Extend the horizontal to the other end of the aqueduct; label this additional distance as "x". Draw another slanty line from the balloon to this other end. Label the angle at the balloon.

Using the height "h" that you found from the first triangle and the angle value, find the length of the base "x + y". Subtract "y" to find the length of the aqueduct.

[mattapus]

Thanks so much for the reply!

I still couldn't get the right answer. Did you manage to get the answer of 299.8 m?

Here's a version of the diagram I'm using to solve the problem. Is this correct?


Again, the help is much appreciated.

[stapel_eliz]

I don't get the book's answer.

[mattapus]

Either did I. I'll have to ask about that in class. Thanks for your time. You didn't happen to get 97.6 m did you?

[stapel_eliz]

Yes, that's what I got.

[mattapus]

It turns out what the textbook meant by "The closest end of the aqueduct is 270.0 m from the balloon", was the horizontal distance between the balloon and aqueduct. Solving this way got me the answer listed. I guess it comes to to interpretation of the wording.

Thanks again for your help!