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Right Triangles and Trigonometry

- Chapter 8

8.1 Geometric Mean

- Geometric mean
- Ex Find the geometric mean between 5 and 45

- Ex Find the geometric mean between 8 and 10

- 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

- The altitude from a right angle of a right

triangle is the geometric mean of the two

hypotenuse segments

B

Ex

A

C

D

- The leg of the triangle is the geometric mean of

the hypotenuse and the segment of the hypotenuse

adjacent

B

Ex

A

C

D

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Find c, d, and e.

Find e and f . (round to the nearest tenth if

necessary)

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

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

- 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

A. Find x.

B. Find x.

- 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.

- 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.

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

- 45-45-90
- The legs are congruent

Ex

Ex

6

x

x

x

8

A.

B.

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Find x and y.

Find x and y.

Find x and y.

(No Transcript)

8.4 Trigonometry In Right triangles

- A. Express sin L, cos L, and tan L as a fraction

and as a decimal to the nearest ten thousandth.

Find the value to the ten thousandth.

- Sin 15
- Tan 67
- Cos 89.6

Find the measure of each angle to the nearest

tenth of a degree

- Cos T .3482
- Tan R .5555
- Sin P .6103

Find y.

Find the height of the triangle.

- 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.

Find angle D.

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?

- 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?

- 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?

- 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?

- 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?