CK-12-Pre-Calculus Concepts

http://www.ck12.org Chapter 4. Basic Triangle Trigonometry

4.8 Applications of Basic Triangle Trigonome-

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Here you will apply your knowledge of trigonometry and problem solving in context.
Deciding when to use SOH, CAH, TOA, Law of Cosines or the Law of Sines is not always obvious. Sometimes
more than one approach will work and sometimes correct computations can still lead to incorrect results. This is
because correct interpretation is still essential.
If you use both the Law of Cosines and the Law of Sines on a triangle with sides 4, 7, 10 you end up with conflicting
answers. Why?

Watch This

MEDIA

Click image to the left for use the URL below.

URL: http://www.ck12.org/flx/render/embeddedobject/58154

http://www.youtube.com/watch?v=-QOEcnuGQwo James Sousa: Solving Right Triangles-Part 2 Applications

Guidance

When applying trigonometry, it is important to have a clear toolbox of mathematical techniques to use. Some of the
techniques may be review like the fact that all three angles in a triangle sum to be 180◦, other techniques may be
new like the Law of Cosines. There also may be some properties that are true and make sense but have never been
formally taught.
Toolbox:

• The three angles in a triangle sum to be 180◦.


• There are 360◦in a circle and this can help us interpret negative angles as positive angles.


• The Pythagorean Theorem states that for legsa,band hypotenusecin a right triangle,a^2 +b^2 =c^2.


• The Triangle Inequality Theorem states that for any triangle, the sum of any two of the sides must be greater
  than the third side.


• The Law of Cosines:c^2 =a^2 +b^2 − 2 abcosC


• The Law of Sines:sinaA=sinbBorsinaA=sinbB(Be careful for the ambiguous case)


• SOH CAH TOA is a mnemonic device to help you remember the three original trig functions:

sinθ=o p phy p cosθ=ad jhy p tanθ=o p pad j

• 30-60-90 right triangles have side ratiosx,x√ 3 , 2 x


• 45-45-90 right triangles have side ratiosx,x,x

√

2