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A2/Trigonometry WINK Sheet

Topic: Trigonometric Applications

TOPIC / STUDY FACTS / SAMPLE PROBLEMS
Law of Cosines to Find a Side: / *Need SAS
Use formula

a = the side you are finding
A = angle opposite the side a
-find a2 (put entire left side of equation in calc in 1 step), then take square root
Law of Cosines to Find an Angle: / *Need SSS
Use formula

A = angle you are finding
a = side opposite the angle A
-Simplify the 3 terms
-Solve for cosA
-Use the inverse cosine function
Law of Sines to Find a Side: / *Need all 2 angles and 1 side
-find the 3rd angle if necessary
(sum of angles in triangle 180o)
Ambiguous Case: / *Use to find the number of triangles that exist, given SSA
-Draw 2 triangles with the given measures
-1: Use law of sines to find a 2nd angle
-2: Find angle by subtracting answer from 1st step from 180
-Test that the sum of the 2 angles is less than 180
-Answer will be 0, 1, or 2
Force Problems: / -Draw 3 vectors: stronger force, weaker force, and resultant force
-Sketch other 2 sides to complete a parallelogram
-Label given info: remember angle between the stronger force and resultant is smaller than the angle btwn the weaker force and the resultant.
-Use properties of a parallelogram to get all info into the bottom triangle.
-Use law of cosines or law of sines to find the missing piece.
-Never use the angle btwn the 2 forces in the trig app…find the supplement for the bottom right angle.
Angle of Elevation and Depression: / -The “double triangle” problems.
-Angle of elevation always on the bottom, looking up.
-Find all angles in both triangles using the linear pair (adds to 180) and the sum of the angles in a triangle.
-Use law of sines to find the shared side, then use law of sines with the other triangle to answer the question.

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