Ch.9 Flashcards
Adjacent
Having a common vertex and side (line that intersects the common vertex)
Acute angle
Less than 90
Scalene triangle
3 sided polygon with Sides that have no equal length
Obtuse
More than 90
Equilateral triangle
3 sided polygon that has all congruent sides
Phythagorean thereom order:
Medium length unknown:
Shortest length unknown:
B
A
Pythagorean triples
3,4,5: 3x,4x,5x
5,12,13: 5x, 12x, 13x
8,15,17: 8x, 15x, 17x
7,24,25: 7x,24x,25x
If a^2 + b^2 > c^2 then abc is an
Acute triangle
If a^2 + b^2 = c^2 then abc is a
Right triangle
If a^2 + b^2 < c^2 then abc is an
Obtuse triangle
Thrm. 9.4: 45-45-90 triangle thereom:
Hypotenuse=
*Leg x √2
* In a 4: 45-45-90 triangle, the hypotenuse is √2 times as long as each leg.
- Thrm 9.5: 30-60-90 triangle thrm.:
- Hypotenuse= shorter leg x ___
- Longer leg= shorter leg x _____
- In a 30 60 90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is √3 x as long as the shorter leg.
- 2
- √3
Opposite (0)
The side across from the reference triangle
Adjacent (A)
Side next to angle
Hypotenuse (H)
Longest side
Trigonometry:
Relationships of the measure’s of right triangles
Theta (0)
Angle measure
Possible ratios:
0/A, A/H, 0/H
Sin =
Sin 0 = 0/H
Cosine =
Cos 0 = A/H
Tangent =
Tan 0 = 0/A
What is the word that reveals the ratios for sine cosine and tangent
Sohcahtoa
Complementary angle =
90
Sin and cos of complement angles are equal when:
Sin (x) = cos (y)
Cos (x) = sin (y)
- Sin A = cos ( 90 - A ) =
- cos A = sin (90 - A) =
- cos B sin B = cos (90- B) = Cosa
- Sin B Cos B = Sin (90- B) = sina
Ex: of cos and sin being similar:
Cos (28) = sin (67)
Cos (28) = 15/17 = A/H
Sin (67) = 0/0 = 15/17
Hypotenuse definition:
Side that is long and opposite to right angle
Opposite definition:
The side that is opposite to the given angle (not the. Right angle)
Adjacent definition:
Side next to given angle
Rounding:
* If the number next to the other number is bigger than make the number ___ ___ ___
* if number next to number is smaller than ____ ____ ____
- one number higher
- remove smaller number
(MISSING ANGLES )Inverse trigonometric ratios:
* inverse tangent : if tan A = x, then tan ^ ___ x = ____
* inverse sine: if sinA = y, then sin ___ y= ____
* inverse cosine: if cos A = Z, then cos ___ Z = ____
- -1, m<A
- -1, m<A
- -1, m<A
Right 🔼
An angle that exactly measures 90 degrees (square)
Isoceles triangle:
A three sided polygon with two congruent sides
Legs
Two sides that form right angle
You can solve a right triangle when you know either of the following:
Two side lengths
One side length and the measure of one acute angle
Find the complement to the following angle
Sin (9)
90 - 9 = 81
Cos (81)
To solve a right triangle means to find all unknown
side lengths and angle measures
Triangle inequality thrm.the sum of the lengths of any two sides are _____ than the length of the third side.
Sides added: the two numbers that are ____ than the biggest number
Third side: ____ number
Greater
Smaller
Bigger
If the two number lengths don’t add up to another number that’s bigger than the third length (biggest side) then it is ____ a _____
Not a triangle
When solving for cos..
X will mostly be put in the left
REMEMBER TRIANGLE TYPES EX. 30-60-90 AND THEIR PROPERTIES B/C IT CAN HELP FIND SIDE LENGTHS
___ ___ ___ is how you will label the triangle with a,b,c
Top left right
__ will mostly be given angle
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