Sine Rule

Sine Rule: A formula used to find a side/angle using its corresponding sides/angles.

The equation corresponds with the  AAS theorem.  It is used when two angles and one side is given or when two sides are given along with one angle. 

The following image shows how the sine rule works and where to plug in the numbers in its appropriate place. The sine rule is one of the most commonly used functions to solve missing sides and angles.

Special Right Triangles

There are two types of special right triangles. The 45-45-90 triangle and the 30-60-90 triangle. The special ability of these triangles is to obtain exact answers without decimal predictions when it comes to trig. functions. Both triangles have their differences besides the angles themselves.

The Difference between 30-60-90 Triangles:

30-60-90 triangles are equilateral triangles split into two pieces. Their side proportions are 1x, 2x, square root of 3x.

45-45-90 Triangles are isosceles triangles. With both of their legs being equal, Their side proportions are 1x, 1x, 2x. Using which ever formula to find the length of the legs, they will be equal no matter what.

Angle of Elevation and Depression

1. The angle of elevation of an object as seen by an observer is the angle between the horizontal and the line form the object to the observer's eye (the line of sight).If the object is below the level of the observer, then the angle between the horizontal and the observer's line of sight is called the angle of depression
2. Angle of Elevation:
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4. Angle of Depression:
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6. Ex:
7. Let x m be the distance of the object from the base of the cliff.

   

   

   

   So, the object is 59.30 m from the base of the cliff.
8. 
   
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Basic Right Triangles

Right Triangle: A triangle with a right angle (90 degrees)
When finding sides and angles in basic right triangles, variables like "x" and "y" are used with opposite angles. To find angles and sides in a right triangle, it is important to remember SOH CAH TOA.
Sin = opposite/ hypotenuse       Cosine = Adjacent/ Hypotenuse      Tangent= opposite/ adjacent
 Also remember for right triangles a^2  + b^2 = c^2

What is Geometry and Trigonometry?

Geometry: the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogs.

Trigonometry: Trigonometry is a branch of mathematics that studies relationships involving lengths and angles of triangles. The field emerged during the 3rd century BC from applications of geometry to astronomical studies.