Heights & Distances Questions and Answers

Directions Give each trig ratio as a fraction in simplest form 1 D Rimeti 29 F 20 E This is a 2 page document work 20 TPI Sin D Cos D Tan D Sin E Cos E Tan E

14 The bottom of a ladder must be placed 3 feet from a wall The ladder is 12 feet long How far above the ground does the ladder touch the wall CH

he smallest positive number for which f x 2x 1 f cos f z 0

Find sin 2x cos 2x and tan 2x from the given information sin x 8 17 x in Quadrant III sin 2x cos 2x tan 2x

1 Explain what a conjecture is 2 How can you prove that a conjecture is false Sec 10 F

A man starts walking north at 3 ft s from a point P Five minutes later a woman starts walking south at 4 ft s from a point 500 ft due east of P At what rate are the people moving apart 15 min after the woman starts walking Round your answer to two decimal places ft s

Simplify the trigonometric expression cos x sin x cos x

Lesson 21 Practice Problems 1 The triangles here are each obtained by applying rigid motion 5 10 N 11 3 12 8 4 2 The quadrilateral is a parallelogram Find the measure of angles 1 2 and 3 13 9 5 14 10 80 6 15 a Which triangles are translations of triangle 17 Explain how you know 11 b Which triangles are not translations of triangle 1 Explain how you know 7

3 How many lines of symmetry exist in each of the flowers below Draw them please

17 reflection across the y axis M W N X 18 reflection across the y axis P g

Write short answers Consider the inverse tangent function defined by y tan xory arctan x Complete parts a d a What is its domain Type your answer in interval notation Simplify your answer Type an exact answer using x as needed Use integers or fractions for any numbers in the expression b What is its range 00 00 Type your answer in interval notation Simplify your answer Type on exact answer using as needed Use integers or fractions for any numbers in the expression c Is this function increasing or decreasing O decreasing O increasing d is there any real number x for which arctan x is not defined If so what is it or what are they O Yes o bo Use a comma to separate answers as needed

Ruben knows triangle ABC and triangle DEC are similar B 43 C E uestion What is the measure of angle DCE What is the measure of angle DCE Skip Question Scratch Paper Optional To Use Functions 7 4 Previous Questi 1 8 AC 5 6 2 3

How does the figure help verify the triangle inequality theorem to 15 A OA by showing that a triangle cannot be formed when the sum of the lengths of two sides equals the length of the third OB by showing that a triangle cannot be formed when the sum of the lengths of two sides is less than the length of the third OC by showing that only one triangle can be formed when the sum of the lengths of two sides is less than the length of the t OD by showing that only one triangle can be formed when the sum of the lengths of two sides equals the length of the third

What single transformation maps AABC onto AA B C A C B B C A 2 0 3 O A rotation 90 clockwise about the origin OB OC O D 0 rotation 90 counterclockwise about the origin reflection across the x axis reflection across the line y x X

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 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

2 5 2 1 1 2 3 5 2 Identify the function whose graph appears above f x la

Point 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

Name 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

E 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

At 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

In 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

While 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

Mike 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

Select 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

You 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

The 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

6 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

For 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

The 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

10 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

Follow 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

31 Find h as indicated in the figure 29 5 392 ft H 49 2 h WAL

35 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

A 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

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

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

The 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

In 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

Choose 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

e 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

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

25 If the circumference of the following circle is 10 II inches find the perimeter of the square inches

Question 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

12 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

The 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

wide 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

Question 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

Identify 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

All 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

15 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