Geometry (Problems 1.)

Question 1

Find the “x” value in the triangle below.

Answer 1

x = 2√3

Question 2

Find the x value in the triangle below.

Answer 2

x = 5

Question 3

Create a Proof for the 45°-45°-90° Triangle Equation

Answer 3

1. Establish that a 45°-45°-90° Triangle has two equal length sides.
2. From that information we can Establish that in the Pythagorean Theorem, A = B, and we can Substitute one with the other.
3. Simplify the equation and solve for A or B to determine that

A = B = (√2/2) C

or

(√2) A = (√2) B = C

Question 4

Find the length of the unknown sides in the triangle shown below

Answer 4

hypotenuse = 8√2

Leg = 8

Question 5

Create a proof for the sides of a 30° 60° 90° Triangle.

Answer 5

1. Create an Equilateral Triangle and label all the sides and angles.
2. Split the Equilateral Triangle down the middle and label the new sides and angles.
3. Create an equation using the Pythagorean Theorem to find the missing side.
4. Solve and Simplify the equation for the missing side “a.”

Question 6

Solve for the missing side of the Triangle.

Answer 6

6√3

Question 7

What is the Sin, Cos, and Tan of angle “F.”

Answer 7

Sin (F) = 12/13

Cos (F) = 5/13

Tan (F) = 12/5

Question 8

Find the missing sides of the triangle

Round your answer to the nearest hundredth.

Answer 8

x = 6.97

y = 5.71

Question 9

Find the missing angle of the triangle

Round your answer to the nearest hundredth.

Answer 9

56.25°

Question 10

Find the missing angle “B”.

Answer 10

angle “B” = 53.68°

Question 11

Find the missing side “AB”

Answer 11

side “AB” = 18.03

Question 12

Find the missing angles

Answer 12

angle “A” = 48.37°

angle “B” = 76.33°

angle “C” = 55.30°

Question 13

Find the missing side “BC”

Answer 13

side “BC” = 8.8

Question 14

What is the Arc Measure, in degrees, of arc (AC) on circle P below?

Answer 14

174°

Question 15

In the figure below, line (DB) and (AC) are diameters of circle P. The length of line (PB) is 8 units.

What is the length of curve (DC)?

Answer 15

(16/3)π

or

16.76

Question 16

In the figure below, the radius of circle p is 10 units. Arc (ABC) has a length of 16π.

What is the measure of Arc (AC), in degrees?

Answer 16

72°

Question 17

Convert the angle Ø = (8π/9) radians to degrees.

Answer 17

160°

Question 18

Convert the angle Ø = 290° to radians.

Answer 18

29π/18 Radians

Question 19

What is the exact length of Curve (BCA)?

Answer 19

85π/2

Question 20

What is the arc measure of Curve (AB), in radians?

Answer 20

17π/30

Question 21

What is the area of the Sector?

Answer 21

27π

Question 22

If angle “ADC” measures 23º, what does angle “ABC” measure?

Answer 22

angle “ABC” = 46°

Question 23

Create a Proof that Triangles created by angles subtending a circles diameter are Right Triangles.

Answer 23

1. Create an image of a random triangle subtending a circles diameter.
2. Cut the triangle in half and label the sides as “r”
3. Realize that the central angle is twice as long as the other angle subtending the same arc and label the angles.
4. Create an equation for the central triangle to determine the other two angles.
5. Once solved, add the theata to the other angle to create a 90° angle

Question 24

What is the Radius of circle “O”

Answer 24

Radius = 8.5 Units

Question 25

The measure of Curve “LI” is 97°, what is the measure of Curve “FL”.

Answer 25

Curve “FL” = 43°

Question 26

What is the length of Line “AC”

Answer 26

Line “AC” = 12 Units

Question 27

What is the measure of Angle “A” ?

Answer 27

Angle “A” = 50°

Question 28

What is the perimeter of Quadrilateral “ABCD” ?

Answer 28

Quadrilateral “ABCD” = 42 Units

Question 29

The equation of a Circle is given below

What is the Center and Radius?

Answer 29

Center = (2/3 , 0)

Radius = 6 Units

Question 30

Write and equation for the circle below

Answer 30

Question 31

The equation of a Circle is given below

What is the Center and Radius?

Answer 31

Center = (0 , 1)

Radius = 10 Units