Triangle Facts

Question 1

30-60-90 Triangle

Answer 1

the sides are -x, x√(3), 2x

so. ..1.) if you know the shorter leg
a) x by √(3) to get the hypotenuse
2. ) If you know the length of the longer leg
a. ) divide it by √(3) to get the shorter leg
b. ) multiply the shorter leg by 2 to get the hypotenuse
3. ) if you know the length of the hypotenuse
a. ) divide it by 2 to get the shorter leg
b. ) multiply the shorter leg by √(3) to get the longer leg

Question 2

Altitude divides an equilateral triangle into…

Answer 2

two 30-60-90 degree triangles
-Let the exterior legs be 2x of the equilateral when an altitude is drawn. The newly formed tri. is a 30-60-90 and the sides are x, 2x, h.

Question 3

An acute angle

Answer 3

is x<90

Question 4

An obtuse angle is…

Answer 4

x>90 and x<180

Question 5

In any triangle..

Answer 5

The longest side is opposite the largest angle.
Shortest side is opposite the smallest angle.
Sides with the same length are opposite angles with the same measure.

Question 6

In a right triangle the sum of the two acute angles…

Answer 6

is 90 degrees.

Question 7

For any positive number x, there is a right triangle whose side are 3x, 4x, 5x.

Answer 7

x = 1  ... 3,4,5
x = 2  ...  6,8,10
x = 3  ...   9, 12, 15
x = 4  ...   12, 16, 20

Question 8

What does the diagonal of a square create?

Answer 8

The diagonal of a square creates two isosceles triangles.

Question 9

What are the sides abstratically in a 45-45-90 triangle?

Answer 9

x, x, x√(2)

Question 10

The only right triangle with integers that you should recognize immediately is…

Answer 10

one w/ sides 5, 12, 13.

Question 11

The measure of an exterior angle of a triangle is…

Answer 11

is equal to the sum of the measures of the two opposite interior angles.

Question 12

If a triangle is a 30-60-90 right triangle then the sides are…

Answer 12

a, 2a (is the length of the longest side) , a√(3)

Question 13

The hypotenuse is not necessarily..

Answer 13

the height

Question 14

A diagonal of a square in effect becomes…

Answer 14

the hypotenuse of each of the two 45-45-90 right triangles formed.

Question 15

The ratio of the length of the hypotenuse to the length of the leg of a triangle formed by a diagonal line across a square is…

Answer 15

√(2):1

Question 16

Any side of a triangle must be…

Answer 16

greater than the difference of the other two sides.

Question 17

In a 30 - 60 - 90 Triangle the sides are

Answer 17

x (Shortest side) , x√(3) (longest side), 2x (hypotenuse)

Question 18

IF you know the length of the shorter leg (x) in a 30 - 60 - 90 triangle then…

Answer 18

1. ) multiply it by √(3) to get the longer leg, and

2. ) multiply it by 2 to get the hypotenuse

Question 19

If you know the length of the hypotenuse in a 30-60-90 triangle (normally x√(3) by in cases where it is known simply x) then…

Answer 19

1. ) Divide it by √(3) to get the shorter leg, and

2. ) multiply the shorter leg by 2 to get the hypotenuse.

Question 20

If you know the length of the longer leg (normally 2x) - normally 2x - in a 30-60-90 triangle then …

Answer 20

1. ) Divide it by 2 to get the shorter leg, and

2. ) Multiply the shorter leg by √(3) to get the longer leg.

Question 21

In a 45-45-90 right triangle the sides are…

Answer 21

x, x, and x√(2)

Question 22

In a 45-45-90 triangle, if the length of the hypotenuse is know then the lengths of the legs can be calculated by…

Answer 22

By dividing the hypotenuse of a 45-45-90 by √(2) the length of the two legs is found

Question 23

An altitude divides an equilateral triangle into…

Answer 23

Two 30-60-90 right triangles.

Question 24

When an equilateral triangle is bisected by an altitude the sides can be defined as…

Answer 24

1. ) The outer legs of the 30-60-90 triangles are 2x
2. ) The altitude becomes h
3. ) The base of the two 30-60-90 triangles are x respectively.

Question 25

The novel pythagorean theorem for a 30-60-90 triangle is…

Answer 25

x^2 + h^2 = (2x)^2

Question 26

Triangle Inequality

Answer 26

1. ) The sum of the lengths of any two sides of a triangle is greater in length than the third side
2. ) The difference of the lengths of any two sides of a triangle is always less than the third side of a triangle.

Question 27

If you are given the length of one leg in a 45-45-90 triangle how can the hypotenuse be determine?

Answer 27

1. ) By multiplying the length of a leg by √(2), you get h.

2. ) By dividing H by √(2), you get the length of each side.

Question 28

The area formula of a right triangle is?

Answer 28

A = (1/2) * (leg1) * (leg2)