Right Triangles and Trigonometry - PowerPoint PPT Presentation

Loading...

PPT – Right Triangles and Trigonometry PowerPoint presentation | free to download - id: 728dc4-ZDk1N



Loading


The Adobe Flash plugin is needed to view this content

Get the plugin now

View by Category
About This Presentation
Title:

Right Triangles and Trigonometry

Description:

The altitude from a right angle of a right triangle is the geometric mean of the two hypotenuse segments The leg of the triangle is the geometric mean of the ... – PowerPoint PPT presentation

Number of Views:68
Avg rating:3.0/5.0
Slides: 37
Provided by: Element64
Learn more at: http://www.cdschools.org
Category:

less

Write a Comment
User Comments (0)
Transcript and Presenter's Notes

Title: Right Triangles and Trigonometry


1
Right Triangles and Trigonometry
  • Chapter 8

2
8.1 Geometric Mean
  • Geometric mean
  • Ex Find the geometric mean between 5 and 45
  • Ex Find the geometric mean between 8 and 10

3
  • If an altitude is drawn from the right angle of a
    right triangle. The two new triangles and the
    original triangle are all similar.

B
A
C
D
4
  • The altitude from a right angle of a right
    triangle is the geometric mean of the two
    hypotenuse segments

B
Ex
A
C
D
5
  • The leg of the triangle is the geometric mean of
    the hypotenuse and the segment of the hypotenuse
    adjacent

B
Ex
A
C
D
6
(No Transcript)
7
Find c, d, and e.
8
Find e and f . (round to the nearest tenth if
necessary)
9
8.2 Pythagorean Theorem and its Converse
  • When and why do you use the Pythagorean Theorem?
  • When given a right triangle and the length of
    any two sides
  • Why to find the length of one side of a right
    triangle
  • When do you use the Pythagorean Theorem Converse?
  • When you want to determine if a set of sides
    will make a right triangle

10
Pythagorean Theorem
c
a2 b2 lt c2 obtuse a2 b2 gt c2 acute
a
b
  • When c is unknown
  • When a or b is unknown

x
5
14
7
3
x
11
  • Converse the sum of the squares of 2 sides of a
    triangle equal the square of the longest side
  • 8, 15, 16
  • Pythagorean Triple
  • 3 lengths with measures that are all whole
    numbers that always make a right triangle
  • 3, 4, 5
  • 5, 12, 13
  • 7, 24, 25
  • 9, 40, 41

Not , so not a right triangle
12
A. Find x.
13
B. Find x.
14
  • A. Determine whether 9, 12, and 15 can be the
    measures of the sides of a triangle. If so,
    classify the triangle as acute, right, or obtuse.
    Justify your answer.

15
  • B. Determine whether 10, 11, and 13 can be the
    measures of the sides of a triangle. If so,
    classify the triangle as acute, right, or obtuse.
    Justify your answer.

16
8.3 Special Right Triangles
  • 30-60-90
  • Short leg is across from the 30 degree angle
  • Long leg is across from the 60 degree angle

Ex
14
x
30
y
17
  • 45-45-90
  • The legs are congruent

Ex
Ex
6
x
x
x
8
18
A.
B.
19
(No Transcript)
20
Find x and y.
21
Find x and y.
22
Find x and y.
23
(No Transcript)
24
8.4 Trigonometry In Right triangles
25
  • A. Express sin L, cos L, and tan L as a fraction
    and as a decimal to the nearest ten thousandth.

26
Find the value to the ten thousandth.
  • Sin 15
  • Tan 67
  • Cos 89.6

27
Find the measure of each angle to the nearest
tenth of a degree
  • Cos T .3482
  • Tan R .5555
  • Sin P .6103

28
Find y.
29
Find the height of the triangle.
30
  • When you need to find the angle measure- set up
    the problem like normal
  • Then hit the 2nd button next hit sin, cos or tan
    (which ever you are using) then type in the
    fraction as a division problem, hit

Find angle P.
31
Find angle D.
32
8.5 Angles of Elevation and Depression
  • Draw a picture and solve using trigonometry.
  • Mandy is at the top of the Mighty Screamer roller
    coaster. Her friend Bryn is at the bottom of the
    coaster waiting for the next ride. If the angle
    of depression from Mandy to Bryn is 26 degrees
    and The roller coaster is 75 ft high, what is the
    distance from Mandy to Bryn?

33
  • Mitchell is at the top of the Bridger Peak ski
    run. His brother Scott is looking up from the ski
    lodge. If the angle of elevation from Scott to
    Mitchell is 13 degrees and the ground distance
    from Scott to Mitchell is 2000 ft, What is the
    length of the ski run?

34
  • An observer located 3 km from a rocket launch
    site sees a rocket at an angle of 38 degrees. How
    high is the rocket at that moment?

35
  • A kite is flying at an angle of elevation of 40
    degrees. All 50 m of string have been let out.
    What is the height of the kite?

36
  • Two buildings on opposite sides of the street
    are 40 m apart. From the top of the taller
    building, which is 185 m tall, the angle of
    depression to the top of the shorter building is
    13 degrees. How high is the shorter building?
About PowerShow.com