# Right Triangle Trigonometry Applications

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```					      Right Triangle Trigonometry Applications

Sin  opp  y    Cos  adj  x                  y
Tan  opp  x
hyp
Csc  opp  1    Sec  hyp  1            adj
Cot  opp  x

Example 1: Find six trig functions for cos  3 .
5

Co-functions of complementary angles are equal.

β

α

Sin α = Cos β
Tan α = Cot β
Sec α = Csc β

To solve a triangle means to find all sides and all
angles.
Example 2: If b=2 and α = 40°, then solve the
triangle.

Trigonometry is used to measure heights and
distances that are either awkward or impossible to
measure by ordinary means.

Example 3: A surveyor needs to measure a river. He
sets up two transit points on each side of the river
(points A & C). Then, he walks east from point C 200
meters to point B. He determines the angle of point B
to be 20°. See illustration on pg. 522. What is the
width of the river rounded to the nearest meter?

Vertical heights are often measured using angle of
elevation and angle of depression.

**Angle of depression is with line of sight and the
horizontal. This is often confused—be careful!

```
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