Right Triangles and Trigonometry

1
Right Triangles and Trigonometry
Similar Triangles are characterized by congruent
corresponding angles and proportionate
corresponding sides. There are several distinct
characteristics of Right Triangles that we will
look at in Chapter 9 that make them very useful
in designing structures and analyzing the world
around us.
2
Finding the Height of a Roof

Y
5.5 h 3.1 Z
W
X
The roof has a cross section that forms a right
triangle. How can we use that information to
determine the actual height of the roof?

6.3 5.5
5.5 3.1 h
h
3.1
2. Then use the proportional component of
similarity to determine the value of h
3
Using Geometric Mean to Solve Problems
4
Using Geometric Mean
5
Trigonometric Ratios
Triangle ABC is a right triangle. The sine
(sin), cosine (cos) and tangent (tan) are defined
as follows sin A side opposite ltA a
hypotenuse c cos A side
adjacent ltA b hypotenuse
c tan A side opposite ltA a
side adjacent ltA b
SOHCAHTOA
6
Finding Trig Ratios
Based upon the SSS Similarity Theorem the two
triangles are similar. What impact do you think
this will have on the Trigonometric ratios?
Large Triangle Small Triangle 8/17
0.4706 4/8.5 0.4706 15/17 0.8824
15/17 0.8824 8/15 0.5333
4/7.5 0.533
7
Trig Ratios for 45o and 30o Angles
In a 45 45 90 Triangle, the Sin, Cos, and Tan
will always fall into a standard proportion to
one another based upon the standard relationship
between the sides (9.4).
8
Solving for a Right Triangle
Solving for a Right Triangle means determining
the measures of every side and every angle - We
can do this if we know The measure of 2
Sides, or The measure of 1 Side and 1 Angle
9
Trig Application Glide Angles and Glide Ratios

• Aerospace Design and landing takes into account
  two concepts based upon Basic Trig Ratios
• Glide Angle
• The angle of approach taken by an aircraft as
  it enters its landing pattern
• Using this angle, pilots and ATC can safely
  guide a plan on a steady descent to its landing
• Glide Ratio
• Mathematical calculation based on the design of
  the aircraft that under specific conditions
  (primarily determined by speed and altitude)
• Determines the distance a plane will travel
  under glide conditions

When an aircraft (Space Shuttle) is at an
altitude of 15.7 Miles it is 59 miles away from
the runway. What is the glide angle of the
approach?
TAN x 15.7 / 59 14.9o
When the shuttle is 5 miles away, it has
increased its glide angle to 19o. What is its
altitude?
TAN 19o h/5 1.7 Miles