This is a contour diagram of a hill with its highest point 200m above sea level. Rings, called contour lines, are drawn at 50m increments along the the hill. These contour lines join all the points that are the same distance above a particular point. In this case, they join all the points that are the same distance above sea level. If the contour lines are projected onto a flat surface, a contour map is formed. The contour map for this particular hill is shown below.¹

Since the contour lines represented heights 50m apart, the height difference between point B and C is 50m. Given the distance between B and a point H (for example), the slope, angle of elevation, and diagonal distance between B and C can be calculated through trigonometric ratios.

Application

On the contour map below, the contour interval is 5m. The horizontal distance between the points X and Y is 1200m. The average slope between X and Y is closest to:

A. 0.0042
B. 0.0125
C. 0.0167
D. 0.0250
E. 0.1250

VCAA Exam 1 2012²

1.  A triangle must be produced in order to represent the relevant data. Point X is 15m above a certain level and point Y is 30m above that same level. That indicates that there is a 15m difference. This information is in red, below.
2. The slope is simply given by:

Hence, the slope for this question can be solved by:

Therefore the answer is D.

See also:

• Bearings
• Angles of elevation and depression

1. Contour maps, Essential Further Mathematics 4th Edition Enhanced, pg 423 ↩

2. VCAA Practice Exams http://www.vcaa.vic.edu.au/Pages/vce/studies/mathematics/further/exams.aspx ↩