Unit 8 Flashcards
In a right triangle with an altitude coming from the right angle, what is the geometric mean formula using h (the altitude)?
x / h = h / y
In a right triangle with an altitude coming from the right angle, what is the geometric mean formula using the legs (a or b)?
x /a = a / c or y /b = b / c
The Pythagorean Theorem only works with what type of triangle?
A right triangle
Give the Pythagorean Theorem
a² + b² = c²
What must c be in the Pythagorean Theorem?
The hypotenuse
Give the Pythagorean Theorem in 3D
d² = l² + w² + h²
What is the requirement about ‘c’ when using the Converse of the Pythagorean Theorem to determine the type of triangle with given side lengths?
c must be the longest side
When using the Converse of the Pythagorean Theorem, what kind of triangle do you have if c² < a² + b² ?
Acute
When using the Converse of the Pythagorean Theorem, what kind of triangle do you have if c² = a² + b² ?
Right
When using the Converse of the Pythagorean Theorem, what kind of triangle do you have if c² > a² + b² ?
Obtuse
When using the Converse of the Pythagorean Theorem, what kind of triangle do you have if a + b < c?
Not a triangle
Give the “names” of the 2 special right triangles.
45°-45°-90° and 30°-60°-90°
What is another name (the proper name) for a 45°-45°-90° triangle?
Isosceles right triangle
In a 45°-45°-90° triangle, how do you go from leg to hypotenuse?
Multiply by √2
Which is the most important side to find in a 30°-60°-90° triangle?
The short leg
In a 45°-45°-90° triangle, how do you go from hypotenuse to leg?
Divide by √2
In a 30°-60°-90° triangle, which leg is the “long leg”?
The one opposite the 60º angle.
In a 30°-60°-90° triangle, how do you go from short leg to hypotenuse?
Multiply by 2
In a 30°-60°-90° triangle, how do you go from short leg to long leg?
Multiply by √3
In a 30°-60°-90° triangle, how do you go from hypotenuse to short leg?
Divide by 2
In a 30°-60°-90° triangle, how do you go from long leg to short leg?
Divide by √3
In a 30°-60°-90° triangle, how do you go from long leg to hypotenuse?
You don’t
In a 30°-60°-90° triangle, how do you go from hypotenuse to long leg?
You don’t
Complete the pythagorean triple: 7,___,25
7, (24), 25
Complete the pythagorean triple: ___, 8, 10
(6), 8, 10
Complete the pythagorean triple: 8,___,17
8, (15), 17
Complete the pythagorean triple: 3,___,5
3, (4), 5
Complete the pythagorean triple: 5, 12,___
5, 12, (13)
Complete the pythagorean triple: 30,___,50
30, (40), 50
Complete the pythagorean triple: 10, ____,26
10, (24), 26
Complete the pythagorean triple: 9, 12, ___
9, 12, (15)
Complete the pythagorean triple: 16, 30, ___
16, 30, (34)
Which do you use when finding angles with right triangle trigonometry– sin, cos, & tan or inverse sin, inverse cos, inverse tan?
inverse sin, inverse cos, inverse tan
Which do you use when finding sides with right triangle trigonometry– sin, cos, & tan or inverse sin inverse cos & inverse tan?
sin, cos, & tan
What is the formula for sin?
sin A = Opposite / hypotenuse
What is the formula for cos?
cos A = Adjacent / hypotenuse
What is the formula for tan?
tan A = Opposite / adjacent
What is the formula for tan? tan A = Opposite / adjacent
What’s the acronym used to help remember those 3 trigonometry formulas?
SOHCAHTOA
When you draw the angle of elevation triangle, what is the most important characteristic?
The horizontal side is on the bottom.
When you draw the angle of depression triangle, what is the most important characteristic?
The horizontal side is on the top.
What is the calculator test to make sure your calculator is able to do right triangle trigonometry properly?
sin(30º) = 0.5
If you get a negative answer when you do sin(30°) on the calculator, what does that imply the error is?
You are in radian mode (the wrong mode)
When is it permissible (in Honors Geometry) to give non-exact values as answers?
When using trigonometry in the problem.
What is the difference between an exact value and a non-exact value?
A non exact value is rounded.
