6.2: Trig. of Right Triangles

1
6.2 Trig. of Right Triangles

• TSW understand and be able to apply the
  definition of the six trigonometric functions
  as ratios of sides of right triangles,
  understand and be able to apply special
  triangles 30?-60?-90? and 45?-45?-90?, and
  understand applications that involve solving
  right triangles at an 85 mastery level as
  demonstrated by discussion and practice.

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Trig. Ratios (SOH-CAH-TOA)
hypotenuse
opposite
adjacent
3
Trig. Ratios

• Ex Find the six trigonometric ratios of the
  angle ? in the figure.
• Ex If , sketch a right triangle with acute
  angle a, and find the other five trigonometric
  ratios of a.

4
Special Triangles

• We can add to our special value chart that the
  following relations are true
• We use a calculator for any other values.
• Ex With our calculator in degree mode, find
• a. b.

5
Applications

• Solving a Right Triangle- to determine all angles
  and side lengths of a given triangle using what
  is given, the trig. ratios, and Pythagorean
  theorem.
• Ex Solve triangle ABC.

B
12
a
30o
A
C
b
6
Applications

• Angles of Elevation or Depression
• Also, useful a r sin ? and b r cos ?
• Ex A giant redwood tree casts a shadow 532 ft
  long. Find the height of the tree if the angle
  of elevation of the sun is 25.7o.

r
a
b
7
Applications

• Ex From a point on the ground 500 ft from the
  base of a building, it is observed that the angle
  of elevation to the top of the building is 24o
  and the angle of elevation to the top of a
  flagpole atop the building is 27o. Find the
  height of the building and the length of the
  flagpole.

8
Applications

• Ex A 40-ft ladder leans against a building. If
  the base of the ladder is 6 ft from the base of
  the building, what is the angle formed by the
  ladder and the building?