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