geocalc final exam

15

DG, EG, and FG, are the perpendicular bisectors of triangle ABC. find each length. AE = 16 AG = 19 CF = 15 find AF.

17

DG, EG, and FG, are the perpendicular bisectors of triangle ABC. find each length. AE = 16 AG = 19 CF = 15 find BD.

19

DG, EG, and FG, are the perpendicular bisectors of triangle ABC. find each length. AE = 16 AG = 19 CF = 15 find BG.

19

DG, EG, and FG, are the perpendicular bisectors of triangle ABC. find each length. AE = 16 AG = 19 CF = 15 find GC.

10

JH = 5y FH = 3y + 4 find the length of the tangent lines.

x = 417 m

Three houses p, q, r are located in the same neighborhood. the distance of p from q is 270 m and the distance to r from q is 236 m. the angle pqr is 111°. find the distance between p and r.

5.5 feet

a 20 foot tree casts a 12 foot shadow. at the same time, a person casts a 3.3 foot shadow. how tall is the person?

118 feet

a bird flying at a height of 55 feet spots a rabbit is at a 25 degree angle of depression from the bird, what is the horizontal distance between the bird and the rabbit?

360°

a circle is _____ all the way around.

false

a kite is a parallelogram

false

a parallelogram is a kite

true

a rectangle is a parallelogram

true

a rhombus is a kite

180°

a semicircle measures _____.

true

a square is a kite

true

a square is a rectangle

true

a square is a rhombus

false

a trapezoid is a parallelogram

lets get this bread

also straight forward

arch measure

central angle is also

ramp is 7.2 feet

chris is building a ramp for a wheelchair that is 12° from the ground and rises to the highest step of 1.5 feet. find the length of the ramp.

DONUT beat AROUND the bush;)

circles r ez dubs

sin(θ) = y/r cos(θ) = x/r tan(θ) = y/r csc(θ) = r/y sec(θ) = r/x cot(θ) = x/y

define the six trigonometric functions in terms of x, y and r.

consecutive angles are supplementary

describe the property of parallelograms that applies to each example:

diagonals bisect each other

describe the property of parallelograms that applies to each example:

opposite angles are congruent

describe the property of parallelograms that applies to each example:

opposite sides are congruent

describe the property of parallelograms that applies to each example:

angle x = angle of elevation angle y = angle of depression

determine the angle of elevation and depression.

bisect

diagonal properties of parallelogram

bisect, congruent

diagonal properties of rectangle

bisect, perpendicular

diagonal properties of rhombus

bisect, congruent, perpendicular

diagonal properties of square

d = √[( x₂ - x₁)² + (y₂ - y₁)²]

distance formula

look at the signs!

don't forget about the square!

clockwise 140°

draw each angle (in standard position): -140°

clockwise 250°

draw each angle (in standard position): -250°

counterclockwise 170°

draw each angle (in standard position): 170°

counterclockwise 520°

draw each angle (in standard position): 520°

θ = 485° θ = -235°

find one positive and one negative angle co-terminal to the given angle: 125°

θ = 610° θ = -110°

find one positive and one negative angle co-terminal to the given angle: 250°

θ = 680° θ = -40°

find one positive and one negative angle co-terminal to the given angle: 320°

θ = 415° θ = -305°

find one positive and one negative angle co-terminal to the given angle: 55°

(-√3)/2

find the exact value of the following trig ratios: cos(210)

√3

find the exact value of the following trig ratios: cot(30)

(√2)/2

find the exact value of the following trig ratios: sin(135)

1/2 + √3

find the exact value of the following trig ratios: sin(150) + 2cos(330)

(-3√3)/2

find the exact value of the following trig ratios: sin(240) + 2cos(150)

(-√3)/3

find the exact value of the following trig ratios: tan(330)

2

find the exact value of the following trig ratios: tan(45) - cot(315)

60°

find the measure of each exterior angle of the following regular polygons: hexagon

45°

find the measure of each exterior angle of the following regular polygons: octagon

72°

find the measure of each exterior angle of the following regular polygons: pentagon

144°

find the measure of each interior angle of the following regular polygons: decagon

120°

find the measure of each interior angle of the following regular polygons: hexagon

135°

find the measure of each interior angle of the following regular polygons: octagon

θ = 20°

find the measure of the reference angle of the given angles: -380°

θ = 40°

find the measure of the reference angle of the given angles: -40°

θ = 55°

find the measure of the reference angle of the given angles: 235°

θ = 80°

find the measure of the reference angle of the given angles: 260°

x = 13 sin A = 5/13 = 0.38 cos A = 12/13 = 0.92 tan A = 5/12 = 0.42

find the missing side length. tell if the side lengths form a pythagorean triple. then find the value of the indicated trig ratios a = 5 b = 12 c = x

sin B = 24/25 = 0.96 cos B = 7/25 = 0.28 tan B = 24/7 = 3.43

find the missing side length. tell if the side lengths form a pythagorean triple. then find the value of the indicated trig ratios a = 7 b = 24 c = 25

2√13

for the given segment ST find the following S(-3,2) and T(1,-4) find the length of the segment.

(-1, -1)

for the given segment ST find the following S(-3,2) and T(1,-4) find the midpoint of the segment.

-3/2

for the given segment ST find the following S(-3,2) and T(1,-4) find the slope of the segment.

ugh okayy

guess what?? you needta know ur 30-60-90 and 45-45-90 triangles! got it??

106°

in kite ABCD, m<BCA = 46° and m<BAD = 56°. find the measurements of the following angles. m<CBA

44°

in kite ABCD, m<BCA = 46° and m<BAD = 56°. find the measurements of the following angles. m<CBD

28°

in kite ABCD, m<BCA = 46° and m<BAD = 56°. find the measurements of the following angles. m<DAC

basically the surface area minus area of the base(s)

lateral area

πrl

lateral area of a cone

4s²

lateral area of a cube

2πrh

lateral area of a cylinder

(2l+2w)h

lateral area of a rectangular prism

none

lateral area of a sphere

((x₁+x₂)/2, (y₁+y₂)/2)

midpoint formula

don't think abt it too much

needta know this

im telling ya! circles r ez!

nice to know

it's just fax

opposite angles add up to 180°

sin(θ) = (5√29)/29 cos(θ) = (-2√29)/29 tan(θ) = -5/2 csc(θ) = (√29)/5 sec(θ) = (-√29)/2 cot(θ) = -2/5

point p is on the terminal side of an angle in standard positions. find the values of the six trigonometric ratios (exact values only). p(-2, 5)

sin(θ) = (-2√13)/13 cos(θ) = (-3√13)/2 tan(θ) = 2/3 csc(θ) = (-√13)/2 sec(θ) = (-√13)/3 cot(θ) = 3/2

point p is on the terminal side of an angle in standard positions. find the values of the six trigonometric ratios (exact values only). p(-3, -2)

sin(θ) = (-3√34)/34 cos(θ) = (5√34)/34 tan(θ) = -3/5 csc(θ) = (-√34)/3 sec(θ) = (√34)/5 cot(θ) = -5/3

point p is on the terminal side of an angle in standard positions. find the values of the six trigonometric ratios (exact values only). p(5, -3)

pythagorean theorem

radius bisector

m = (y₂- y₁) / (x₂- x₁)

slope formula

the measurement of the outer surface of an object

surface area

πrl+πr²

surface area of a cone

6s²

surface area of a cube

2πrh+2πr²

surface area of a cylinder

2lw+2lh+2wh

surface area of a rectangular prism

4πr²

surface area of a sphere

510 meters

the angle of elevation from a boat to the top of a 90 meter hotel is 10°. how far is the boat from the base of the hotel?

1/2

the radius is _____ the diameter.

width = 31.8 inches height = 42.4 inches

the size of a TV screen is given by the length of its diagonal. the screen aspect ratio is the ratio of its width to its height. the screen aspect ratio of a standard TV screen is 4:3. what are the width and height of a 53" TV screen? round your answer to the nearest inch.

false

true or false: a rectangle is a square

false

true or false: a rhombus is a rectangle

x = 2.55 ft

use a calculator and trigonometric ratios to find each length. round to the nearest hundredth theta = 27° opposite = x adjacent = 5 ft

x = 12.46 m

use a calculator and trigonometric ratios to find each length. round to the nearest hundredth theta = 62° opposite = 11 m hypotenuse = x

x = 19.70 mm

use a calculator and trigonometric ratios to find each length. round to the nearest hundredth theta = 62° opposite = 11 m hypotenuse = x

x = 22°

use inverse trig functions to find the angle measures below theta = x adjacent = 52 hypotenuse = 56

x = 36°

use inverse trig functions to find the angle measures below theta = x opposite = 14 hypotenuse = 24

x = 39°

use inverse trig functions to find the angle measures below theta = x opposite = 34 adjacent = 42

x = 38°

use inverse trig functions to find the angle measures below theta = x opposite = 34 hypotenuse = 55

also know 0° and 90°

use the unit circle to complete the table.

b = 28.0 c = 33.0 A = 29°

using the law of sines (los) or the law of cosines (loc) solve the following triangles. round the angle measures to the nearest degree and the side lengths to the nearest tenth: a = 16 B = 58° C = 93°

A = 55° B = 43°

using the law of sines (los) or the law of cosines (loc) solve the following triangles. round the angle measures to the nearest degree and the side lengths to the nearest tenth: a = 24 b = 20 c = 29 C = 82°

A = 137° B = 17° C = 26°

using the law of sines (los) or the law of cosines (loc) solve the following triangles. round the angle measures to the nearest degree and the side lengths to the nearest tenth: a = 9 b = 6 c = 14

c = 33.0 B = 31° A = 58°

using the law of sines (los) or the law of cosines (loc) solve the following triangles. round the angle measures to the nearest degree and the side lengths to the nearest tenth: b = 17 a = 28 C = 91°

97.2°

what is the measure of swimming?

43.2°

what is the measure of tennis?

a chord

what is this showing?

a diameter

what is this showing?

a radius

what is this showing?

a secant line

what is this showing?

a tangent line

what is this showing?

don't be a dum dum

yo u should know regular or irregular and concave or convex polygons