Geometry Questions

Use the information given about the angle 0 0 2x to find the exact value of each trigonometric function tan 0 8 sin 0 0 0 a sin 20 b cos 20 c sin d cos 02 a sin 20 Type an exact answer using radicals as needed e tan 20 f tan 0 2

3 A hiker whose eye is 1 6 metres above ground stands 50 metres from the base of a vertical cliff The angle between the line connecting her eye and the top of the cliff and a horizontal line is 58 a Draw a diagram representing the situation b Find the height of the cliff

angles with the following sides are right angled triangles a 9cm 40 cm 41 cm b 10 m 24 m 26 m c 10 10 200 d 11 2 7 5 8 3 3 The spiral in the figure is made by starting with a right angled triangle with both legs of length 1 unit 1 1 1 11 1 a Find the hypotenuse of the first triangle Then the second right angled triangle is built with one leg measuring 1 unit and the other leg being the hypotenuse of the first triangle b Find the hypotenuse of this second triangle A third right angled triangle is built on the second triangle s hypotenuse again with the other leg measuring 1 unit c Find the hypotenuse of the third triangle The process is continued in the same fashion and the hypotenuse of the final triangle is denoted by x d Find the length of x 4 A right angled triangle has a hypotenuse of 8 2 cm and another side length of 4 3 cm Draw a diagram Calculate the area of the triangle Give your answer correct to 1 dp

Determine the length of each arc with radius r and central angle a given below Give your answer correct to 2 dp a r 5 cm 70 b r 4 cm 45 c r 10 5 cm a 130 The London Eye is a giant Ferris wheel in London It is the tallest Ferris wheel in Europe with a diameter of 120 m The passenger capsules are attached to the circumference of the wheel and the wheel rotates at 26 cm per second a the length that a passenger capsule would travel if the wheel makes a rotation of 200 b the time in minutes that it would take for a passenger capsule to make a rotation of 200 t the time to the nearest whole minute that it would take for a passenger capsule to make a full revolution

1 Determine the length of the unknown sides for each of the right angled triangles below b 10 2 9 cm 61 2 Z I Z y 34

A door with width 4 20 m has an arc as shown in the diagram Find a b The radius of the arc to the nearest cm The length of the arc to the nearest cm 225 4 20 m

different regions in 1985 and in 2005 Population in Population 1985 in 2005 4 9 10 6 4 109 1 1 x 10 1 3 x 109 7 6 x 108 1 1 109 2 4 108 3 0 108 8 9 x 106 7 2 x 106 Place Entire world China India United States Bulgaria a Determine the ratio of the population of the entire world to that of China in 2005 giving your answer to the nearest integer b Find the increase in the world s population between 1985 and 2005 c Calculate the percentage change in the population of each of the four countries giving your answers accurate to 3 sf List the countries according to their percentage change from highest to lowest d State whether or not you agree that it

ops drop of

nas abo 15 drops One drop of

7 In an experiment the probability that event A occurs is and the probability that event B 8 occurs is 334 If A and B are independent events what is the probability that A and B both occur Simplify any fractions

3 The image of a speck of dust viewed through an electron microscope is 1 2 x 10 millimetres wide The image is 5 x 102 times as large as the actual size Determine the width in millimetres of the actual speck of dust

Determine the magnitude and direction of the vertical shift and the phase shift for the function below f x cos x 7 Select the correct answer below The vertical shift is units up and the phase shift is 1 units right The vertical shift is 1 units down and the phase shift is The vertical shift is 1 units down and the phase shift is The vertical shift is 1 units up and the phase shift is units left O The vertical shift is units down and the phase shift is 1 units left The vertical shift is 1 units up and the phase shift is units right 1 units left units right

2 In 1856 Andrew Waugh announced Mount Everest to be 8840 m high after several years of calculations based on observations made by the Great Trigonometric Survey More recent surveys confirm the height as 8848 m Calculate the percentage error made in the earlier survey 4 The temperature today in Chicago is 50 F Instead of using the standard conversion 5 formula C x F 32 Tommaso uses his grandmother s rule which is easier but gives an approximate value Subtract 32 from the value in F and multiply the result by 0 5

Find the percentage error in using 3 14 instead of 7

3 With 72 million bicycles correct to the nearest million Japan is at the top of the list of countries with most bicycles per person On average Japanese people travel about 2 km by bicycle correct to the nearest km each day Calculate the upper bound for the total distance travelled by all the bicycles in Japan per day 4 To determine whether a business is making enough profit the following formula is used P C S C S where P is relative profit S is sales and C is costs If a company has 340 000 worth of sales and 230000 of costs correct to 2 significant figures calculate the maximum and minimum relative profit to the ate

A triangle has a base length of 3 1 cm and corresponding height 4 2 cm correct to 1 decimal place Calculate the upper and lower bounds for the area of the triangle as accurately as possible 4 2 cm 3 1 cm

Find the range of possible values for the following measurements which were rounded to the nearest mm tenth of m and hundredth of kg respectively b 3 2 m c 1 75 kg a 24 mm

State two other ways to name Zx T y X U

a Use Gauss elimination method to solve the following problem A shopkeeper is selling 3 types of fruits namely mango guava and pineapple By selling 3 kg of mangoes 1kg of guava and 2 pineapples he made a gain of 35 By selling 2 kg of mangoes 3kg of guavas and 1 pineapple he made a gain of 10 By selling 2 kg of guavas and 1 pineapple he made a loss of 5 How much profit or loss will he make if he sells 3 kg of mangoes and 2 pineapples b For which real values of a and b the matrix 20 bl becomes orthogonal

33 The perimeters of two similar figures are 20 in and 50 in What is the ratio of the areas of the two figures State your answer as a fraction 34 If triangle ABC is similar to triangle MNO and side AB 23 when side MN 10 what is the length of side BC when side NO 33 O 72 03 O 77 94 O 75 9 O 74 26

2 Use the following similar triangles AABC ADEF If BC 26 when EF 29 and DF 13 what is the length of the corresponding side to DF Solve mathematically drawings not to scale Round your answer to the nearest tenth AC A B D F E

2 3 The perimeter of this figure is O 11 in 15 in O 16 in 12 in2 O 12 ft 16 ft 2 1 and the area is 2

a Asked to name the distance that corresponds to the height slant height and base of parallelogram DEBT Brian and Briana Bronco wrote down different answers How they differed on identifying the base is shown below Complete the chart with rest of their answers slant height base height Briana TD Brian Find the area and perimeter of DEBT DE T B 6 G 65 9 7 2 D F 77 E 7 5 Measurements are in inches When they calculated the perimeter and area of DEBT did the Bronco twins Brian and Briana get different answers Explain

y 6 25 Points Given that the pair of triangles is similar find the lengths x and y Let a 4 and b 13 X DETAILS Need Help a b STRIG2 B 1 011 Read It 3 2 y 2 2

W 1 Volume of cubes prisms and pyramids JUB What is the volume of this triangular pyramid 6 m Submit 9 m 10 m cubic meters

e table below gives the shape and color of toy blocks in a certain set ese are the only toy blocks in the set Shape Star Square Circle Triangle Clover Color Purple Green Red Blue Red conditional statement is given below Give the converse contrapositive and inverse of the statement Also use the table abc ecide if each statement is true or false Assume that any toy block mentioned comes from the set Given statement If a toy block is a triangle then the toy block is blue Converse Contrapositive Inverse If Choose one then Choose one If Choose one then Choose one If Choose one then Choose one O True True True True False False False False X

The midpoint of ST is M 3 0 One endpoint is S 6 5 Find the coordinates of the other endpoint T T M 3 0

In the figure below g o Find the values of x and y g m 70 3y 26 x O X y

ZABD and ZDBC are A B What is the measure of x D 7 complementary angles X x C Angles are not drawn to scale Enter

7 Jaime randomly surveyed some students at his school to see what they thought of a possible increase to the length of the school day The results of his survey are shown in the table below Lengthening School Day Survey In Favor Grade 9 10 11 12 12 15 8 5 Opposed 6 3 12 16 Undecided 9 11 10 9 Part A A newspaper reporter will randomly select a Grade 11 student from this survey to interview What is the probability that the student selected is opposed to lengthening the school day Part B The newspaper reporter would also like to interview a student in favor of lengthening the school day If a student in favor is randomly selected what is the probability that this student is also from Grade 11

Use the graph to answer the question Y T S Q 2 4 2 N 2 R 29 Which ordered pair corresponds to point U 30 Which ordered pair corresponds to point S 31 Which point is located in Quadrant II

1 Measure the line segments below in 2 Use your protractor to draw ZABC with measure of 155

16 If AB 12 and AC 5x 4 find x MWO SE alle atmoe niwe www P

16 If AB 12 and AC 5x 4 find x MMO Trades armloq gniwollst B

3 4 Name the plane that represents the bottom of the box Find the intersection of DC and CF Find the intersection of planes EDCF and BGFC Name the two planes that intersect at EF Shado plano CBG 0144 D A sipas telleme E H C B F

2 3 of DE is 3 5 The coordinates of D are 1 5 What are the coordinates of E GADS PIRE JEAS List all segments that are parallel to DE List one segment that is skew to AB xod sids D E F G

8 a 9 10 Are the following points collinear QNM circle one Yes No b Are the following points coplanar Q NP circle one Yes No Name line a in two other ways Name one pair of opposite rays N M a

15 If mZPOS 2x 5 and mZSQR 3x 10 a b Find x to engad to notrpensinilants bali S 0909 10 to nolasetain ads unit Find the measure of the smaller angle Al is there in baill anstadt ame P

Find the distance between Importa Box

Match the following number sequences to the formulas 5 10 20 40 5 10 15 20 4 8 16 32 4 8 12 16 DRAG DROP THE ANSW a 5 5n an 4 2 1 an 4 4 n 1 an 5 5 n 1 an 5 2

20 Name the following in the diagram below Intersection of 2 Segments Intersection of 2 planes 1 L sc ban 21 P nouammolni nsvig sdt In diw og does am Two skew segments d What is a Vertex SACS 08 CA POR M R TA OA SOTH STAD OR Om Tr

19 Are these polygons Give a reason why or why not BAC to A od D E B B to swesom sa brit of torq Day 320 30 C SASA DAS A HACS 2 A E HACE Isdal nedi bus w of two fastsan 9000f om oss C 08935 001 ON 8 stuz6em navig adi daw signe ross

Classify 7 Sides 09 4 sides the PolygoN 12 sides please 9 Sides Smal sielamos of trigins surgit sri sau 2 1 292075 207 BASS to ABS te

For Exercises 13 15 find the measure of the angle formed by the hands at each time 13 3 00 14 4 00 19 15 3 30 10 9 8 12

K For Exercises 1 5 use the figure at right to complete each statement of ZBAE 1 A is the Mid Paint 2 AD is the Ray 3 AD is a 4 If mLBAC 42 then mLCAE 5 LDAB DAE of LBAE of LDAE no vriw no Seasure of D

K For Exercises 16 and 17 mark each figure with all the given information 16 mLADB 90 AD BD LDAB LDBA A B D C 17 m RPQ 90 QR TZ RT QZ LQ LT R 47 P T 3673879 xemay

For Exercises 10 12 use your protractor to draw and then label each angle with the given measure 10 mLMNO 15 11 m RIG 90 12 mLz 160

P is the weighted average of A and B on the number line Find the coordinate of P under the given conditions 5 4 3 2 1 0 1 2 4 1 A has a weight of 6 and B has a weight of 3 2 The weight of A is one third the weight of B 3 The weight of B is 0 and the weight of A is greater than 0

Peas are measured by diameter Determine the area of a 6 inch personal pizza Round your answer to the nearest hundredth AN of square inches Determine the area of a 14 inch personal pizza Round your answer to the nearest hundredth 18394 osquare inches A6 inch personal pizza has 580 calories Determine the number of calories in the 14 inch poza Round your answer to the nearest calorie There are calories in the 14 inch pizza A 14h plas cut into 8 slices Estimate the number of calories in one slice of a 14 inch plesa Round your answer to the nearest calorie

If carpet costs 16 65 per square yard and is available in whole square yards only find the cost of carpeting the three bedroom floors in the accompanying floor plan Click the icon to view the floor plan It will cost to carpet the three bedroom floors www