2D Geometry Questions and Answers

19 28 Solving a Triangle Use the Law of Sines to solve for all possible triangles that satisfy the given conditions 19 a 28 b 15 LA 110 20 a 30 c 40 LA 37 21 a 20 c 45 LA 125 22 b 45 c 42 LC 38 23 b 25 c 30 LB 25 2i bud sill of 197132

5 As shown in the diagram below a ladder 12 feet long leans against a wall and makes an angle of 72 with the ground Label missing sides using different variables a Find to the nearest tenth of a foot the distance from the wall to the base of the ladder b Find to the nearest tenth how high the ladder leans against the building 12 ft

1 Using the right triangles ABC GEF and IHJ below to complete the trig ratios below 1 G 12 13 a sin A d tan F E 5 g cos 5 4 b cos A e cos G B 3 A h tan I b tan C f sin F 2 H 5 JI

What are the horizontal shift and vertical shift of this equation y x 3 2 5

Solve the system using row operations X y Z 4x 4y 3z 2y 3x 4z 3x 3y 6z 5 12 21

Graph the equation and state the slope d x 3

8 10x 1 14 13x 1 18 6x s4 54 X 42 42 42 12 12 X

Solve for x Assume that lines which appear tangent are tangent 18 12 12 PO 8 x 7 27 X 5

This design began from the construction of a regular hexagon A Describe a rigid motion that will take the F E H B D

In quadrilateral QUAD QDUA and QU DA U What additional information would be sufficient to prove that quadrilateral QUAD is a rectangle A B QR RA and DR RU QA DU QA 1 DU

A helicopter makes a forced landing at sea The last radio signal received at station C gives the bearing of the helicopter from C as N 57 0 E at an altitude of a 440 feet An observer at C sights the helicopter and gives DCB as 13 9 How far will a rescue boat at A have to travel to reach any survivors at B See the figure below Round your answer to the nearest 10ft W

22 B 29 A E 54 29 F C Triangle ABC and Triangle DEF each have an angle measuring 29 and an angle measuring 54 as shown above Which of the following statements is sufficient to prove triangle ABC is congruent to triangle DEF 54 D A The length of EF is 10 B The measure of angle EDF is 97 C The length of BC is equal to the length of EF D The measure of angle BAC is equal to the measure of angle EDF

The line y 2x 2 is perpendicular to line 1 If these two lines have the same y intercept which of the following could be the equation of line 1 A y 2x 2 B y 2x 2 1 C y x 2 1 D y x 2

A A sin A B sin B C tan A D tan B a b B Given the right triangle ABC above which of the following is equal to a C

2 y 2 10 di A 6 The graph of line I is shown in the xy plane above Which of the following is an equation of a line that is parallel to line 1 2 A y x 2 3 2 B y x 10 x 3 C y x 4 D y 3x 1

A 60 B 70 to Note Figure not drawn to scale In the figure above i 50 and k 140 What is the value of 7 C 80 D 90 jo

a b C 13 In the diagram AB CD What is the value of a b 80 A 60 140 40 20 a C B D o 10

1 2 If the length of a base of right triangle and the hypotenuse of triangle DEF is 8V5 units what is the length of the other base a 4 units b 8 units c 8V 2 units d 16 units e 32 units

Questions 37 and 38 refer to the following information The population of a small town is currently 800 A statistician estimates that the population of the town will decline by 14 percent per year for the next five years The statistician models the population P of the town after x years using the equation P 800 k 37 38 In the equation above what value should be used for k According to the statistician s model what will the population of the town be to the nearest whole number after five years

A 30 D B O 50 E C In the figure above line segment AC is tangent to the circle with center O at point B Line segments AO and CO intersect the circle at points D and E respectively If the circumference of circle O is 72 what is the length of minor arc DE

Diameter A is 18 cm and diameter B is 6 What is the ratio of circumference A to circumference B 18 6 3 not enough information

What is the sector area of a sector created by circle with a radius of 2 m and a 140 central angle Figure may not be drawn to scale 14 m 4 5 m 77 9 292 75 2 m A B 140 2 m

Questions 23 25 refer to the following information A team of scientists measures the volume of various samples of different gases with a constant pressure of 0 1 atm and a constant temperature of 610 K The graph below plots the volume of each sample against the amount of the gas 23 Volume liters 2 88 89 90 120 100 80 60 40 20 last0 Volume Amount Relationship Among Samples of Gases 0 5 1 1 5 Amount moles 2 Sample S 2 5 The Ideal Gas Law predicts that at this pressure and temperature the volume of an ideal gas can be modeled by the equation V 50n where V is the volume in liters and n is the amount of the substance measured in moles Assume that the relationship is valid for greater amounts of the substance than are shown in the graph A mole is approximately 6 022 102 molecules According to the data provided what is the volume in milliliters of Sample S A 8 104 B 2 x 10 C 8 x 10 D 4 x 10 There moles of vol A 25 B li

Question 8 1 point N M 14m L 21 82 26 9 80 43 64 10m K What is the length of segment LN

26 Let the polynomials fand g be defined by f x 3x 6x 11x and g x 8x 15x 7 Which of the following polynomials is divisible by 3x 7 A j x 2f x g x B k x f x g x C m x f x 2g x D n x f x 3g x

A car factory that operates 24 hours a day and 7 days a week produces one car every 20 minutes How many cars does the factory produce in 3 days

A scientist estimates that the water level of a lake is dropping by 2 25 inches per year If this trend continues how many years will it take for the wate level in the lake to drop by 27 inches

4a j 7a 3 4b k 7b 3 In the equations shown above j and k are constants jis k plus 1 which of the following is true 1 3 A a is b plus B a is b minus D 1 3 C a is b minus 1 a is b minus 3

P Q y R Given the right triangle PQR above which of the y following is equal to X A cos P B cos Q C tan P D tan Q

B A C D Group A Group B Total 21 38 4 50 Number of Times Watching the News per Week Never 3 4 Total 21 50 38 100 7 4 11 1 2 The table above shows the results of a survey in which 100 people were asked how often they watched the news Group A consisted of people who were registered voters and Group B consisted of people who were not registered to vote If one person is randomly chosen from among those who watch the news fewer than three times a week what is the probability that the person was a member of Group A 14 13 27 18 21 39 More than 4 11 12 23 50 50 100 in the graph A made in

2 Determine the value of DE and EF to the nearest SI bns 0 011 saunatagyd or al 3 algasin dgh to woln 3 C 70

STRETCH IT In triangle JKL below mzJ 58 2 and JK 5 4 What is the relationship between JK and the angle Adjacent Opposite or Hypotenuse J 18 biswau 2900 K

An airplane is on a heading of 075 at 250 km h and an 85 km h wind is blowing from 300 Determine the resultant velocity of the airplane using Cartesian vectors and state the groundspeed and bearing of the resultant

tch a graph from factored form include zeros and bounces bends crossing nts o x 2 x 6 x 4

1 Calculate the son of interior ongles of a heptagon 7 gon 3 Solve for x 5 2 regular 15 gon 4 Solve for x 1 5

A triangle is placed in a semicircle with a radius of 9 mm as shown below Find the area of the shaded region Do not round any intermediate steps Round your final answer to the nearest hundredth and be sure to include the correct unit If necessary refer to the list of geometry formulas 19 mm 0 mm Xx mm mm

O Points 0 of 1 Opomba is sitting on a sled on the side of a hill inclined at 30 The combined weight of Ojemba and the sled is 100 pounds What is the magnitude of the force required fir Mandisa teep the sk Miding down the hill SA

Justin is filling a container with unit cubes Each cube measures exactly 1 cubic inch He places the first 9 cubes on the bottom of the container as shown below 3 inches B 3 inches How many unit cubes in total must Justin use to fill the container C 3 inches D 9 unit cubes 36 unit cubes 18 unit cubes 1 cubic inch 27 unit cubes

The curves of the 2 functions are given as follows f x x 5x 6 g x 4 3x x a b c Determine the 2 interception points of the above curves Hint f x g x 10 marks Find the interception points of f x and g x on the x axis and y axis 12 marks 3 marks Sketch the curves

r Flanagan made a line plot to show the number of hours the 15 students in his class spent doing homework last night 5 O Number of Students Labu 0 5 Number of Students Number of Students Time Spent Doing Homework udents 0 xxxxxxxxx X 1 2 3 4 0 5 5 Number of Hours Time Spent Doing Homework XX 1 5 XXXXXXXX 2 3 4 5 5 5 Number of Hours x 1 5 XXXX Time Spent Doing Homework XXXXXXXXX x 2 3 4 5 5 Number of Hours 1 X 1 X 1 Time Spent Doing Homework of the students spent 5 of an hour doing homework Which line plot could be the one Mr Flanagan made

Which statement is TRUE about a unit cube O O O A C Its volume is equal to 1 unit plus 1 unit B Its volume is equal to 1 unit plus 1 unit plus 1 unit C Suspe Its volume is equal to 1 unit times 1 unit Its volume is equal to 1 unit times 1 unit times 1 unit

At the park there is a pool shaped like a circle A ring shaped path goes around the pool Its inner radius is 11 yd and its outer radius is 15 yd 11 yd 15 yo We are going to give a new layer of coating to the path If one gallon of coating can cover 6 yd how many gallons of coating do we need Note that coating comes only by the gallon so the number of gallons must be a whole number If necessary refer to the list of geometry formulas gallons of coating Espa ol Aa

A rotating light is located 19 feet from a wall The light completes one rotation every 3 seconds Find the rate at which the light projected onto the wall is moving along the wall when the light s angle is 10 degrees from perpendicular to the wall light wall feet per second

Use the graphs below to answer questions 1 4 PROPERTIES OF TRANSFORMATIONS 6 5 4 GIOVANNI D F XAN F 6 5 4 1 F HANNAH B ENT B Describe the transformation represented on Hannah s graph cansione Rotation over y axis ABC A B C er Giovanni s graph write a 1 and a 2 o the 1st and 2nd transformations in the ence of transformations represented by aph Not all choices will be used a Reflection over x axis 5 Translation 4 units right Rotation 180 clockwise Rotation 90 clockwise Translation 4 units left D graph s represent a pre image that is nt to the image and which graph s Is a pre image that is similar to the H G ANDREW 7 I 3 For Andrew s graph write a 1 and a 2 next to the 1st and 2nd transformations in th sequence of transformations represented his graph Not all choices will be used 1 a Dilation by a scale factor of b Rotation 90 clockwise c Translation 6 units up d Dilation by a scale factor of 4 e Translation 6 units left 5 Ricardo will transform a triangle con quadrant II by reflecting over the x axi dilating by a scale factor of 0 5 Which true statement A The image will be in quadrant III

3 5 3 1 6 Solve for x and y Leave answer as a simplified Radical 1 2 X 60 20 30 Y X 5 3 60 30 X Y 4 30 X 6 X 60 30 60 9 14 3 Y X 9

5 How far from the base of the house would you need to place a 15 ft ladde so that it reaches the top of a 12 foot wall Draw a picture then solve

Solve for x Round to two decimals if necessary 13 cm 15 cm X

Identify if the following sides form an acute obtuse or right triangle 11 in 13 in 5 in O a Ob Oc Acute Obtuse Right

45 y Solve for y O a Ob Oc Od 10 5 5 2 10 2 5 3

Solve for x Round to two decimals if necessary X 13 cm 15 cm PREVENT X PLACE