Name: ____________________
Geol 351- Geomath
Using Trig to Solve Problems in Geology
In-Class and Take Home Problems (Set 1)
1. Given a triangle with hypotenuse of length 1, and sides of length x and y as shown
below, define the various trigonometric functions;
sin() = ______
cos() = ______
tan()=______
cot()=______
sec()=______
csc()=______
1
y

x
2. Convert the following angles from degrees to radians:
a) 30 degrees
b) 45 degrees
3. Convert the following angles from radians to degrees:
a) 0.5
b) 1.2
4. At the base of a cliff you are standing on top of geological Unit A. The cliff face is
formed along a normal fault (nearly vertical). The top of Unit A is also exposed at the top
of the cliff face. You walk a distance x = 200 feet away from the fault scarp. Looking
back toward the cliff, you use your Brunton and measure and note that the top of the cliff
is 23o above the horizon. What is the offset along this fault?
h

x
x
Cliff
Face
5. In the example illustrated below, a stream erodes less resistant fault gauge leaving an
exposed fault scarp on the distant bank. You are unable to traverse the stream or make
your way to the top of the exposure. Using your Brunton compass, you stand on the left
edge of the stream and measure the angle (a) formed by the top of the cliff and the
horizontal. You walk to the left 175 feet and measure angle (b). Angle a measure 31o and
angle b, 19o. How can you determine the cliff height? What is the width of the stream?
Fault
Scarp
h
b
d
a
x
Stream
6. Using the diagram and results from problem 2 assume the cliff face is capped by a
resistant sandstone layer. The sandstone is underlain by less resistant shale which has
been eroded by the stream. 38.4 feet of sandstone are exposed on the upper cliff face.
The shale is exposed on the left bank of the stream and has a dip of 30o. What is the
thickness of the shale bed?
7. The three point problem uses elevations measured at three points on a stratigraphic
surface to determine the strike and dip of that surface. The elevations and locations of
these points can be measured at the surface or, more likely, in the borehole. In the
following problem, you have data from three boreholes (located in the map below)
indicating subsea depths to the top of the Oriskany Sandstone as shown.
Determine the strike and dip of the Oriskany surface.
-4700’
N
-4300’
-5000’
Scale: 1:10000
Take Home Problem
8. Solve Question 5.9 in Waltham given as: Two exposures, 500 m apart, are 400m and
200m, respectively, from a church. Calculate using equations 5.17, 5.19, and 5.20, the
angles contained by the triangle defined by the two exposures and the church. Use
Waltham’s Excel file Trig.xls (see http://www.gl.rhbnc.ac.uk/~dave/ sheets/Trig.xls or
pick up the files from the H:\Drive) to confirm your result.
Show work for 8 on back