# Trigonometry Question, Finding the distance and angle of elevation.

So there is this question, and for some reason, whether it be the early time of day or my lack of skills, It seems I have no idea how to draw the required diagram. I have tried and tried but none of them seem right. Here is the question. $$\text{From point A, 93m due south of the base of a tower, the angle of elevation} \\ \text{is 35 degrees. Point B is 124m due east of the tower. Find: } \\ \text{a) The height of the tower, to the nearest metre.} \\ \text{b) The angle of elevation of the tower from point B.}$$

I know that if I knew what the diagram looked like I could complete the question, I have also searched and searched and could not find any worked solutions, although I know that $a) = 65m$ and $b) = 27.7 \text{ degrees}$. Could anyone please help me visualise the diagram in which this question is unclearly (in my case) referring to? Thanks in advance!

• Are you sure those answers are correct for your problem? My calculation for a yielded a different result. André's answer below should help you finish the problem If you need more visualization, try this – MrCMedlin Jul 19 '14 at 3:40
• According to my textbook, yes :). However, if you do find an error please do tell me because these things are possible! Thank you! – Samir Chahine Jul 19 '14 at 3:42
• Sorry, the answers you posted are correct. My calculator was in "radians" mode! :O – MrCMedlin Jul 19 '14 at 3:49
• It's all good! At least you had an answer, I was clueless for over 20 minutes, haha. Thanks anyway! :) – Samir Chahine Jul 19 '14 at 3:53

## 1 Answer

There will be two entirely separate diagrams.

Diagram 1: Draw a horizontal line segment $AP$, $A$ on the left, $P$ on the right. The point $A$ is the observer, the point $P$ is the bottom of the tower. Now draw a vertical line segment $PQ$, with $PQ$ perpendicular to $AP$. The point $Q$ represents the top of the tower. Join the points $A$ and $Q$ by a straight line.

Diagram 2: Almost the same, except the bottom line segment is $BP$.

Label your diagrams with distances, angles. For instance, $AP=93$, and $\angle QAP$ is $35$ degrees.

I hope this is enough for you to finish things. After drawing the diagrams, do make sure to look back on the problem and see how your pictures connect with it. It turns out that the South and East stuff is irrelevant for the calculation.

• +1 here. The information about one point being due south and another being due east is distracting and irrelevant when it comes to diagramming this solution. – MrCMedlin Jul 19 '14 at 3:46
• Thank you! Found the answers pretty easily, do you have any tips on telling whether or not some points in a question are just distractions, such as "south" and "east" in this question? Thanks again! @andré-nicolas – Samir Chahine Jul 19 '14 at 3:52
• You are welcome. No tips, really. Just visualize the tower, the observer at $A$. Then the tower, and the observer at $B$. The first line (separate diagrams) is there because a good three-dimensional representation would be difficult to draw, and is not really needed, we are solving separate two-dimensional problems. – André Nicolas Jul 19 '14 at 3:58
• As André said, you'll want to think about the simplest way to solve the problem. You do need both point $A$ and point $B$, since they're asking you two different questions, but it's important to recognize they aren't both needed at the same time. It might help to think about the question in terms of what information is needed to solve it, and then looking back into the problem for that information. – MrCMedlin Jul 19 '14 at 4:03