# Geometry Questions

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Geometry

Solution of trianglesFind a cofunction with the same value as the given expression csc 5 Select the correct choice below and fill in the answer box to complete your choice Simplify your answer Type any angle measures in degrees Do not include the degree symbol in your answer A csc 5 tan csc 5 sec 85 Oc csc 5 cot OD csc 5 sin

Geometry

Heights & DistancesFollow the instructions for each problem Figures shown are NOT drawn to scale 1 If AB 48 and BC 22 then AC 2 3 5 7 9 11 A JL 84 If JK 5x 8 and KL 4x 4 then x FG 8x 4 If GH 4x 8 and FH 15x9 then FG F S B T is the midpoint of SU If ST 16 then SU A G If AB 18 and AC 3x 6 then x B Green 39 H If DE 7x 3 and EF 9x 19 then EF 4 Purple 60 6 8 If DF 51 and EF 32 then DE 12 D R RT 60 If RS 2x 1 and ST 4x 7 then x P PQ 2x 3 If QR 5x 7 and PR 10x 11 then PR E S 10 If TU x 7 and UV 5x 13 then UV T D is the midpoint of CE If CE 28 then DE Match the question number with the answer below Color the picture accordingly Blue 57 Orange 12 Orange 19 Green 8 F R If QR 8x 1 and QS 20x 26 then RS R E Blue 32 Yellow 10

Geometry

2D GeometryUse the figure below to find the exact values of the half angles 5 Find sin cos and tan sin cos tan 11 12 0

Geometry

2D GeometrySTATE The toco toucan Ramphastos toco is the largest member of the toucan family and possesses the largest beak relative to body size of all birds This exaggerated feature has been interpreted in various ways such as being a refined adaptation for feeding However the large surface area may also be an important mechanism for radiating heat and hence cooling the bird as outdoor temperature increases Here are data for beak heat loss as a percent of total body heat loss at various temperatures in degrees Celsius Temperature C 15 16 17 18 19 20 21 22 Percent heat loss 32 34 35 33 37 46 55 51 from beak Temperature C 23 24 25 26 27 28 29 30 Percent heat loss from beak 43 52 45 53 58 60 62 62 access the complete data set click the link for your referred software format cel Minitab14 18 Minitab18 JMP SPSS TI R Mac KT PC TXT CSV Crunchlt rom a graph in G J Tattersall et al Heat exchange from the toucan bill als a controllable vascular thermal radiator Science 325 2009 pp 470 O Macmillan Learning PLAN Plan to create a scatterplot and compute a numerical correlation metric to analyze the relationship between percent heat loss from beak response variable and temperature explanatory variable SOLVE Use software of your choice to create a scatterplot of percent heat loss from beak versus temperature Examine the scatterplot and describe the pattern Identify the correct interpretation of the relationship between temperature and percent heat loss based on the scatterplot r There is a weak negative linear relationship between temperature and heat loss There is a strong positive linear relationship between temperature and heat loss There is a moderately strong positive nonlinear relationship between temperature and heat loss O There is a weak negative linear relationship between temperature and heat loss Calculate the correlation r between temperature and the percent of heat loss from beak Provide your answer with precision to three decimal places

Geometry

2D GeometryUse the figure below to answer items 15 through 17 given that A B C D 8 points each P P1 B4 D4 A4 C4 T B Du C P3 P2 B2 1 T 2 K B3 L4 D3 C3 16 C4 B4 D4 A4 P3 P2 CA D4 17 A4 D4 C4 B4

Geometry

Area17 Mia has 80 m of fencing material and would like to fence a rectangular plot o Determine the a dimensions of the plot that would ensure maximum area b maximum area that can be enclosed with 80 m of fencing material c the domain and range for the area function

Geometry

Heights & Distances35 Height of an Antenna A scanner antenna is on top of the center of a house The angle of elevation from a point 28 0 m from the center of the house to the top of the antenna is 27 10 and the angle of elevation to the bottom of the antenna is 18 10 Find the height of the antenna

Geometry

Area1 Pin 2n Zn 26 A 29 4 5 1 0 13 13 23 21 2 25 1 3CH 28 26 F v T 27 a v COS sin 12 i 2 iv 0 v 6 cot 14 d iv g viii and 35 D 39 B 43 D 11 21m viii 6 and 0 ix a circle ii F vi T b i e ii b vii 29 No 33 27 B 30 False 2x 3 NIO EXEMPLAR PROBLEMS MATHEMATICS 36 C 40 A 44 D 2 P n 1 2 3 28 A 5 3EXERCISE NIM Fa 3 0 2 30 15 vi vii 0 x 2 3 21 i T vii F c 1 vi 4a 1 37 B 41 A 45 B 34 Real axis 38 A 42 B 31 2 3 21 46 2 B iv T vii F be repubished hed

Geometry

Coordinate systemThis question 1 point s possible Sketch an angle 8 in standard position such that has the least possible positive measure and the point 3 3 is on the terminal side of 0 Then find the values of the six trigonometric functio for the angle Rationalize denominators if applicable Do not use a calculator Choose the correct graph below OA B Select the correct choice below and if necessary fill in the answer box to complete your choice O C O D Submit quiz

Geometry

Coordinate systemO A 18 Sketch an angle 0 in standard position such that has the least possible positive measure and the point 6 8 is on the terminal side of 0 Then find the exact values of the six trigonometric functions for 0 p 18 18 9 X 18 A o OB 18 Ay 18 9 9 18 X 18 nus pos This question 1 point s possible Select the correct choice below and if necessary fill in the answer box to complete your choice O C possible 18 9 18 Ay 19 19 W 18 18 Submit quiz 5

Geometry

Coordinate systemThe terminal side of an angle 8 in standard position passes through the point 2 1 Use the figure to find the following value cos e cos 8 Type an exact answer in simplified form Rationalize all denominators

Geometry

2D GeometryLines m and n are parallel and are intersected by transversal line 1 1 5 E m 2 6 3 4 8 7 If the m 1 71 what is the measure of its corresponding angle Type the correct answer in the box Use numerals instead of words For help see this worked examp

Geometry

Coordinate systemConsider two displacement vectors defined by their magnitudes and directions as follows A has a magnitude of 37 0 m and is directed in the direction B has a magnitude of 52 0 m and is directed 33 0 clockwise from the direction Let C A B What is the direction of C Note Express your answer as an angle

Geometry

2D GeometryYou will explore the relationships between corresponding angles when two parallel lines are cut by a transversal Directions Read the instructions for this self checked activity Type in your response to each question and check your answers At the end of the activity write a brief evaluation of your work Activity In this activity you will use the GeoGebra geometry tool to explore the relationships between the corresponding angles formed when a transversal cuts two parallel lines Open parallel lines and transversals and complete each part of the activity For help watch this video about using measurement tools in GeoGebra Part A Measure and record all eight angles formed between the transversal line EF and the parallel lines AB H and CD Take a screenshot of your diagram showing the measures of all the angles and paste it in the space below BIUX X 15px AVV EEEEEE HY

Geometry

Coordinate systemWrite the standard form of the quadratic function whose graph is a parabola with the given vertex and that passes through the given point Let a be the independent variable and y be the dependent variable Vertex 6 21 point 7 0 X

Geometry

Coordinate systemhe figure to the right shows the feasible set of a transportation problem and the straight line of all ombinations of shipments for which the transportation cost is 108 Complete parts a through c elow D feasible set a The objective function is cost 288 3x 2y Give the linear equation in slope intercept form of the line of constant cost c 3 Simplify your answer Do not factor Use integers or fractions for any numbers in the equation A C B y x 0 Q

Geometry

2D Geometrythe triangle below LF is a right angle Suppose that mz E 5x 16 and mz G 4x 20 G F 4x 20 45x 16 E a Write an equation to find x Make sure you use an sign in your answer Equation b Find the degree measure of each angle mLE 0 mLF m G 0 0 X X S

Geometry

2D Geometrym the triangle below suppose that m 2 V 2x 9 mz W 7x 1 and m2 X x ind the degree measure of each angle in the triangle 2x 9 W 7x 1 X m V m2 W mLX 0 0 0 O X

Geometry

Coordinate systemNote In case the lines L and L do not pass through the origin we may take lines L and L which are parallel to L and L respectively and pass through the origin If instead of direction ratios for the lines L and L direction cosines namely 1 m n for L and l m n for L are given then 1 and 2 takes the following form cos 0 1 mm nn as m 1 m n and sin 0 1 m 1 m m n m n n 1 1 4 Two lines with direction ratios a b c and a b c are i perpendicular i e if 0 90 by 1 ii parallel i e if 0 0 by 2 a a by C Now we find the angle between two lines when t acute the angle between the lines then aa bb ce 0 F a Ab and F b b b B In Cartesian form if 0 is the angle between the lines 3 3 2 2 b cos8 4 not to cos 8 19 T M cos 8 9 56 3 4 12 19 3x7 21 X X y 2 2 and a by where a b c und a b c are the direction ratios of the lines 1 and 2 respectively then Example 7 Find the angle between the pair of lines given by F 3i 2 4k M 2 2k aa bb cc b b c Rationalised 2023 24 and 7 57 2j 37 2j 6k Solution Here 7 23 2k and h 3i 2 6k The angle 8 between the two lines is given by bb 2 2k 37 27 6k THREE DIMENSIONAL GEOMETRY equations are given If 0 is 1 4 4 9 4 36 3 Hence 0 cos Example 8 Find the angle between the pair of lines x 3 y 1 2 3 published 4 ched 1 2 385

Geometry

Coordinate systemDraw a line representing the rise and a line representing the run of the line State the slope of the line in simplest form de o Click twice to plot each segment Click a segment to delete it 5 7 k 3 10 6 9 00 N Un 3 a M M 02 C T 700 56 Y 8 10

Geometry

3D GeometryE The diagram shows a vertical pole PQ which is supported by two wires fixed to the horizontal ground at A and B Find a b BQ 40 m PBQ 36 BAQ 70 ABQ 30 the height of the pole PQ the distance between A and B 70 A 360 og 300 B

Geometry

2D GeometryIn the triangle XYZ XY 14 cm XZ 17 cm and angle YXZ 25 A is the foot of the perpendicular from Y to XZ Calculate a the length XA b the length YA c the angle ZYA

Geometry

Coordinate systemUse the diagram to the right If AD 16 and AC 2y 2 find the value of y Then find AC and DC What is the value of y y Type an integer or a decimal Find AC and DC Type an integer or a decimal DC Type an integer or a decimal AC A E D B C

Geometry

2D Geometry6 Complete the statement that best describes the intercept of your graph when the quantity The value of the quantity zero Please select a valid drop area is value unit is

Geometry

2D Geometryne time increases 1 s for every 1 cm of speed moices Reset S 0 time 27705 6277 cm position Submit Answer X unlimited submissions remaining speed

Geometry

Solution of triangles20 A ray that divides the angle into two angles is the angle bisector 21 An obtuse triangle has exactly one angle whose measure is greater than 90 biosoqsil 22 Suppose a set of thin rods is glued together into a triangle as shown How would you place the triangular arrangement of rods onto the edge of a ruler so that they balance Explain why

Geometry

2D Geometry10 ABC ikizkenar dik gen DC AB AC 1 BC AC BC AB BD Yukar daki verilere g re m AED x ka derecedir A 50 B 60 C 62 D 70 A E B E 75

Geometry

3D Geometry17 An acute angle is an angle whose measure is less than 90 18 If two lines intersect to form a right angle then the lines are perpendicular 19 A diagonal is a line segment that connects any two vertices of a polygon

Geometry

Heights & DistancesA national automobile association determines that the mean fuel consumption for vehicles in a particular state is 23 6 miles per gallon with a standard deviation of 5 8 miles per gallon If a Normal model is applicable approximately what percent of vehicles in that state should get between 28 and 30 9 miles per gallon Use a calculator or a Normal distribution table to help calculate your answer to the nearest tenth of a percent A 10 4 B 12 0 C 30 9 D 22 4

Geometry

AreaX is normally distributed random variable with mean 63 and standard deviation 6 The probability that X lies between 45 and 81 is Note Write your answer as a decimal rounded to the nearest thousandth

Geometry

Coordinate systemhe following balance sheet for the Los Gatos Corporation was prepared by a recently hired accountant In reviewing the statement ou notice several errors Cash Accounts receivable Inventory Machinery net Franchise net Total assets LOS GATOS CORPORATION Balance Sheet At December 31 2024 Assets Liabilities and Shareholders Equity Accounts payable Allowance for uncollectible accounts Notes payable Bonds payable Shareholders equity Total liabilities and shareholders equity 44 000 86 000 57 000 122 000 32 000 341 000 54 000 7 000 59 000 112 000 109 000 341 000 Additional Information 1 Cash includes a 22 000 restricted amount to be used for repayment of the bonds payable in 2028 2 The cost of the machinery is 194 000 3 Accounts receivable includes a 22 000 notes receivable from a customer due in 2027 4 The notes payable balance includes accrued interest of 7 000 Principal and interest are both due on February 1 2025 5 The company began operations in 2019 Net income less dividends since inception of the company totals 37 000 6 52 000 shares of no par common stock were issued in 2019 200 000 shares are authorized equired repare a corrected classified balance sheet Use the additional information to help determine appropriate classifications and account

Geometry

3D Geometry3 3 If two secants P and PC of a circle meet the circle at A B and C D respectively then PA x PB PC x PD 6 Ac

Geometry

2D GeometryR H K C M La b N Name a point that is collinear to point L 1 Points have to be in capital letters Name another name for line b Name the intersection of line c and plane R Name a point that is non coplanar to plane R Name a side of HKL Ray start at the vertex and continue out Hint Hint Rays have to

Geometry

2D GeometryWhich angles are adjacent angles B E H F C A ZBCF and BCA ZBCF and ZGFH D G ZBCF and ZEFC ZBCF and GFC

Geometry

2D GeometryThe midpoint of AB is M 1 3 If the coordinates of A are 3 1 what are the coordinates of B

Geometry

2D GeometryBD and EG are parallel lines B E A C F ZDCA and LGFC HA ZDCA and GFH D Which angles are adjacent angles G ZDCA and DCF ZDCA and LEFC

Geometry

2D GeometryCE and FH are parallel lines C F B D G LCDG and ZEDB I LCDG and ZFGI E Which angles are corresponding angles H LCDG and ZCDB LCDG and ZFGD

Geometry

AreaWhich angles are alternate exterior angles F I E G ZIJL and ZFGJ ZIJL and ZHGJ H K ZIJL and ZHGE ZIJL and ZFGE

Geometry

2D GeometryConsider the following graph of a linear equation 6 5 Find the slope of the line m T Find the y intercept Enter a point 6 5 4 3 2 0 1 3 2 1 0 1 2 3 4 5 6 2 3 3 0 5 6 Enter the equation of the line written in slope intercept form y mx b

Geometry

2D Geometry2 A B and C are the centers of the 3 circles How many equilateral triangles are there in this diagram B

Geometry

2D Geometry4 If m23 54 find each measure a m1 b m 2 c m 4 d m25 e m26 5 11 12 14 13 f m27 g m28 h m 9 i m 10 j m 11 k 1 m212 m 13 m m 14

Geometry

Coordinate systemTriangle ABC has the following coordinates A 1 1 B 5 4 C 4 1 and Triangle ABC will be translated 3 units right and 6 units up 1 Write a coordinate rule to describe the translation 2 What will be the coordinates of the image of point A