# Heights & Distances Questions and Answers

Geometry

Heights & DistancesTitle Construct a triangle given that the perimeter is 115 mm the altitude is 40 mm and the vertical Description Construct a triangle given that the perimeter is 115 mm the altitude is 40 mm and the vertical angle is 45 Construct a triangle with a base measuring 62 mm an altitude of 50 mm and a vertical angle of 60 Now draw a similar triangle with a perimeter of 250 mm Title Construct a triangle given that the perimeter is 115 mm the altitude is 40 mm and the vertical Description Construct a triangle given that the perimeter is 115 mm the altitude is 40 mm and the vertical angle is 45 Construct a triangle with a base measuring 62 mm an altitude of 50 mm and a vertical angle of 60 Now draw a similar triangle with a perimeter of 250 mm

Geometry

Heights & DistancesPoint A is a vertex of a polygon Point R is the image of A after the dilation Find the scale factor of the dilation 11 A 2 3 and R 10 15 9 A 3 4 and R 9 12 10 A 9 12 and R 6 8

Geometry

Heights & DistancesName Dilations Worksheet State whether a dilation with the given scale factor is a reduction or an enlargement 1 k 3 2 k 1 3 N 3 k 5 4 4 k 0 93

Geometry

Heights & DistancesE A 60 B 41 In the diagram AGEF and AHEF are congruent What is the value of x C 28 H D 30 60 2 x 2 LL F

Geometry

Heights & DistancesAt the beginning of the lesson Jacob determined that there was a problem with the sail length measurements of 7 5 meters 4 8 meters and 2 5 meters Explain how Jacob was able to determine there was a problem with the specifications of the triangular sail BIUX X 15px V AVV

Geometry

Heights & DistancesIn the invoice that specifies the side lengths of the triangular sail as 7 5 meters 4 8 meters and 2 5 meters suppose the mistake was in the length of 2 5 meters Determine the range of values that are possible for the third side length x of the sail BI U X X 15px V A v B

Geometry

Heights & DistancesWhile sailing Jacob is 150 feet from a lighthouse The angle of elevation from his feet on the boat at sea level to the top of the lighthouse is 48 What can you conclude about the height of the lighthouse with respect to Jacob s distance from the lighthouse Explain your answer BIUX X 15px A

Geometry

Heights & DistancesMike is designing two sails for Jacob Help him determine the range of possible lengths of the third side of each sail Part A The first sail has one side of length 9 feet and another side of length 6 feet Determine the range of possible lengths of the third side of the sail BIUX X 15px V A Space used includes formatting 0 15000 Submit A BY Part B The second sail has one side of length 22 feet and another side of length 2 feet Determine the range of possible lengths of the third side of the sail BIUX X 15px

Geometry

Heights & DistancesSelect the correct answer from the drop down menu Manuel is building a frame for a triangular table He has four pieces of wood measuring 8 feet 3 feet 5 feet and 12 feet What pieces can Manuel combine to make the frame Manuel could only use the pieces that are 8 ft 3 ft and 5 ft 8 ft 5 ft and 12 ft 8 ft 3 ft and 12 ft 3 ft 5 ft and 12 ft in length

Geometry

Heights & DistancesYou will experimentally verify the relationship between side lengths and angles in triangles using geometry software Directions Read the instructions for this self checked activity Type in your response to each question and check your answers At the e of the activity write a brief evaluation of your work Activity Use GeoGebra to explore side angle relationships in triangles and to complete each part For help watch this short video about using GeoGebra measurement tools Part A Use the distance or length tool to add side lengths to the triangle Then use the move tool to drag vertex C to make it the largest angle and then the smallest angle What happens to the side opposite vertex C when it is the largest angle The smallest angle Type your answer in the box

Geometry

Heights & DistancesThe diagram below shows a helicopter hovering at point H 380 m vertically above a lake Point A is the point on the surface of the lake directly below the helicopter helicopter 380 H 40 B 25 diagram not to scale Minta Minta is swimming at a constant speed in the direction of point A Minta observes the helicopter from point C as she looks upward at an angle of 25 After 15 minutes Minta is at point B and she observes the same helicopter at an angle of 40 a Write down the size of the angle of depression from H to C

Geometry

Heights & Distances6 What if a restaurant needed to build a wheelchair ramp for its customers The angle of elevation for a ramp is recommended to be 5 degrees If the vertical distance from the sidewalk to the front door is 2 feet what is the horizontal distance that the ramp will take up x How long will the ramp be z Round your answers to the nearest hundredth 3 points z 2 09ft x 61ft

Geometry

Heights & DistancesFor Exercises 2 6 match the term on the left with its figure on the right 2 Trapezoid 3 Rhombus 4 Rectangle 5 Kite 6 Parallelogram E B F For Exercises 7 10 sketch and label the figure Mar 4 D

Geometry

Heights & DistancesThe sun is 18 above the horizon Find the length of a shadow cast by a park statue that is 12 feet tall Round your answer to one decimal place ft

Geometry

Heights & Distances10 The contractor you are working for needs to know the height of a building to see if his 300 foot crane will reach the top If you read an angle of inclination of 40 13 52 at a distance of 350 ft from the base of the building what is the building height and will the crane reach the top Draw a neat diagram

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

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

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

Heights & Distances1 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

Geometry

Heights & Distancesdifferent 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

Geometry

Heights & DistancesThe endpoints of two segments are given Find the length of each segment If necessary round your answers to the nearest tenth EF E 1 1 F5 1 and GH G 3 1 H 1 6 The length of EF is Tell whether the segments congruent 24 Yes 25 O No If they are not congruent tell which segment is longer The length of GH is about O EF is longer GH is longer O EF and GH are congruent The coordinates of the midpoint of GH are Ms 0 and the coordinates of one endpoint are H 2 9 The coordinates of the other endpoint are Find the distance between the points C 6 5 and D 3 1

Geometry

Heights & DistancesIn the right triangle find the length of the side not given Give an exact answer and an approximation to three decimal places 4 a 6 c 10 a The exact value of b is Type an exact answer using radicals as needed www

Geometry

Heights & DistancesChoose the best selection for the quadrilateral with vertices at the following points 1 0 5 0 1 3 5 4 Hint Start by graphing the points Distance Formula d x2 x y2 y A Parallelogram B Trapezoid C Rhombus D Rectangle

Geometry

Heights & Distancese viewing angle 0 of an object is the angle the object forms at the lens of the viewer s eye The viewing angle is related to the object s height H and distance from the viewer D through the formula tan 2D A forest ranger views a tree that is 160 feet away with a vie gle of 18 How tall is the tree e height of the tree is approximately feet

Geometry

Heights & DistancesUse a reference angle to write sec 25 in terms of the secant of a positive acute angle in radians 36

Geometry

Heights & Distances25 If the circumference of the following circle is 10 II inches find the perimeter of the square inches

Geometry

Heights & DistancesQuestion 31 Find the midpoint of the line segment joining the points 1 2 and 1 2 O 0 0 Points 2 O 1 2 O 1 2 O 2 1

Geometry

Heights & Distances12 Check to see if the sides are proportional by creating ratios between corresponding sides and reducing the fractions Shortest Sides 5 Middle Sides Longest Sides 13 13 Are the two triangles gimilar Similar

Geometry

Heights & DistancesThe length of a rectangle is 8 inches more than its width Set up an equation to find the width of the rectangle if the area is 32 sq inches Owx 8 32 Ow 8 w 32 Ow 8 w 32 w 8 w 32

Geometry

Heights & Distanceswide is it O 2 ft O 1 ft O 3 ft O 4 ft ectangular mat is 16 feet It is 6 feet long How

Geometry

Heights & DistancesQuestion 2 Points 3 A 42 inch wire is bent into the shape of a rectangle whose width is twice its length Set up an equation to find the length of the rectangle O 2 21 1 42 O 21 1 42 O 21 1 2 42 O 21 1 42

Geometry

Heights & DistancesIdentify the geometrical name of the object shown below By lidar Sagdejev Spedious GFDL http www gnu org copyleft id html or CC BY SA 4 0 https creativecommons org licenses by sa 4 0 from Wikimedia Commons Rectangular prism O Triangular prism Hexagonal prism

Geometry

Heights & DistancesAll changes a Two buildings building A and building B are 200 and 1000 feet tall respectively The two building are placed side by side and a telephone wire is connected from the top of building A to the top of building B creating a 20 a from building B to building A Building A is on the left and building B is on the right 12 What is the difference in the heights of the two buildings Height Difference feet 13 We want to know how far apart the buildings are Which trigonometric ratio could we use with the given information to find the missing distance 14 Find the distance between the two buildings 20

Geometry

Heights & Distances15 40 B 75 ft Ashley you are standing 75 ft away from the base of a tree and using your awesome powers of deduction and the proper geometric tools you ve figured out that the angle of elevation from the ground to the 40 4 Describe the process that you d go through to solve for the height of the tree using the given information i U Font Family AA A FEE EB

Geometry

Heights & DistancesProblem 60 Let f x y 4 y to answer the following A Explain why the cross section for the surface z f x y produced by cutting it with planes parallel to x 0 are semicircles of radius 2 B Describe the cross sections of the surface in the planes y 0 y 2 and y 3 C Describe the surface z f x y

Geometry

Heights & Distances5 Rectangle A is dilated to form rectangle B A 6 e 20 B 30 Target due 10 31 23 39 5 75 What scale factor was used Enter the answer and also provide a 1 sentence explanation that describes how you determined your answer Review the rub you will be evaluated

Geometry

Heights & DistancesEXTRA CREDIT The units are in yards Find the area of the shaded region Ashaded Region Tyd

Geometry

Heights & Distances10 The volume of the right rectangular prism is V 270 cm Write a quadratic equation in terms of x Don t solve the equation 2 points x 3

Geometry

Heights & Distances9 A lot for sale in a subdivision has the shape of the quadrilateral shown in the figure Find the area the lot rounded to two decimals 10 points 75 ft 800 40 ft 135f 128 ft

Geometry

Heights & DistancesA ball is thrown from an initial height of 4 feet with an initial upward velocity of 40ft s the ball s height in feet after seconds is given by the following Find all t values of for which the ball s height is 26 feet

Geometry

Heights & Distanceshe what you w ciple Part II 19 Points 1 A e radius of a circle is 5 mm then find the area of the Posttest O 5 square mm O 10 square mm O 15 square mm O 25 square mm Complete

Geometry

Heights & DistancesMatch the equation with the sentence Susanne was hiking down from Mt Whitney She started at 14 500 ft above sea level and descended 375 ft every 30min Kirk was hiking up to Mt Whitney He started at 7545 ft above sea level and ascended to the top 14500 ft after about 8 5 hours of hiking Using an average pace choose the function that describes his elevation relative to the time in hours Jolie was hiking up to Mt Whitney She started at 7545 ft above sea level and ascended to the top 14500 ft after about 10 hours of hiking Using an average pace choose the function that describes her elevation relative to the time in hours Juan was hiking down from Mt Whitney He started at 14 500 ft above sea level and descended 1400 ft every hour Choose Choose E t 70 3 t 14500 E t 818 81 7545 E t 6961 7545 E t 75 6 t 14500 Choose Pedro loves to try new adventures His most recent adventure was jumping out of an airplane His special watch tells him his altitude He set a timer at the moment he opened

Geometry

Heights & DistancesTutorial Exercise The Cartesian coordinates of a point are given a 7 7 1 Find polar coordinates r 8 of the point where r 0 and 0 0 2 ii Find polar coordinates r 8 of the point where r 0 and 0 0 2 b 5 5 3 i Find polar coordinates r e of the point where r 0 and 0 0 2 ii Find polar coordinates r e of the point where r 0 and 0 0 2

Geometry

Heights & DistancesSolve the equations for solutions in the interval 0 360 Use a calculator for Problem 12 give the answer to the nearest hundredth of a degree 9 Sin x 1 3 10 Sec x 2Sec x 0 11 2cos x root 3 0 In degrees just verifying I am doing this correctly Trigonc Sub subj Sear

Geometry

Heights & DistancesUse fundamental identities to find the values of the trigonometric functions for the given condition sec 0 6 and tan 0 0 sin 0 cos 0 tan 0 cote sec 0 CSC 0

Geometry

Heights & DistancesQuestion 6 Find the distance between A and B 6 4 2 Points 2 20 Y 18 16 14 12 10 8 6 4 2 0 4 5 O 5 units O 6 units O 7 units 8 units 2 A 4 4 6 8 B 10 12 14 16 18 20 X