Geometry Questions

Graph the data you obtain from your experiment

Tools Jared is constructing a rectangular door for a shed If the door shown below has a width of 42 in and a diagonal support of 94 in what is the approximate height of the door 7 O O A B D 52 in 84 in 103 in 136 in ABC

Option A 1 Design an experiment to collect data that can be modeled as a parabol

Tools Question 10 Consider this right triangle Enter the ratio equivalent to tan L tan L Symbols 13 7 8 N 5 M 9

3 Determine the equation that best fits the data and graph that as well

8 Tools Consider this right triangle N Read the question and type your response in the box provided Your 22 22034 M Enter the measure of ZM to the nearest degree

the question and type your response in the box provided Your response will be saved automatically On the diagram below a boat represented by point A is 450 feet away from a buoy represented by point B Another buoy is located at point C The three points form a right triangle with the measure of A equal to 21 3 A 21 3 450 ft Enter the distance between the two buoys rounded to the nearest foot feet

Tools Find the correct equation to solve for m m 53 A B C D 24 124 cos 53 tan 53 tan 53 cos 53 24 m m 24 24 m 2024 Illuminate Education TM Inc

Tools X Read the question and type your response in the box provided Your Consider this right triangle 17 30 Enter the value of side length x

Tools Question 6 Use the table below to determine the approximate height of the flag pole 35 2024 25 ft A B C 14 3 ft 17 5 ft 20 5 ft D 35 7 ft sin 35 0 57 cos 35 0 82 tan 35 0 70 Illuminate Education TM Inc 4

Tools O Question 4 Which pair of equations can be used to solve for x in A PQR P A B C D 18 Q 57 sin57 cos57 sin57 tan57 R 18 18 18 x and cos33 18 and sin33 1 18 18 x and cos33 and cos33 18

Tools Question 1 Right triangle XYZ is shown below Z 29 20 X 21 Enter the ratio equivalent to tan X 2024 Illuminate Education TM Inc

Tools A B C 6 Which trigonometric ratios are equivalent to Select TWO that apply U 10 cos P sin P cos R 8 sin R R

State whether the following measures can be side lengths of a triangle Click Yes or No for each situation A 4 4 7 B 2 9 12 C 3 5 8 D 10 12 15 Yes Yes Yes Yes No No No No

Question 9 G A B C K 6 JG 13 N M II Pause 7 ZJ 7 ZH 7 and ZG 7 ZJ 7 but not ZH or ZG Q Zoom

4 Question 7 AJKL is shown below Choose the correct option that has the angle measures from least to greatest K 6 8 cm A B C D 8 9 cm ZK ZJ ZL ZJ ZL ZK ZJ ZK ZL ZL ZK ZJ II Pause Q Zoom 2024 Illuminate Education Inc 5 2 cm L

4 H Using the information provided select the triangle congruence criterion that can BEST be used to prove that AHFGA HKJ A angle angle side AAS angle side angle ASA side angle side SAS side side angle SSA B C D C2024 Illuminate Education Inc

Which of the following is NOT a valid Triangle Congruence Theorem A SSS B C ASA SAS

Which congruence postulate or theorem shows that the triangles Welow are congruent 38 15 A B 100 AA AAS ACA 100 15 380

In the figure shown PSRQ Which theorem can be used to prove ASQR AQSP P 0 00 A B C S R SAS Congruence Theorem SSS Congruence Theorem AAS Congruence Theorem

csc0 1 Cose csc 1 Multiple Simplify the following csc0 1 trigonometric expression by following the indicated direction by

19 YT 9 Find TW W X T Z

Use the DESMOS software to complete the following questions 1 Complete the table below by graphing using DESMOS software Vertex y x 5 y x 2x 3 x 2x 3 y 2x 5x 3 y 2x 4x 7 Direction of opening Maximum Minimum Axis of symmetry x intercepts y intercept

5 Triangle ABC has been dilated from center D to form triangle RST 10 7 5 R S Is AGRS AART Explain 25 A T 12 cm C If the length of the segment AC x which is the length of the segment RT Date 10 6 In the diagram below GRS ART GR 36 SR 45 AR 15 and RT 18 G 36 A 45 15 R A 10 cm 18 Alex designed a plan for a large mosaic wall including a scale model below T 9 R 1 C 88 45 30 6 20 15 25 2 25 The wall is 10 m wide and 7 m high What are the dimensions of the largest mosaic he can make on that wall Explain He will use 2 cm square tiles to make his mosaic How many tiles will he need Explain how you found your answer 316 AJA Jus

A O Qo B Suppose that line segment A B is the image of line segment AB after a dilation with a scale factor of 0 5 centered at point Q Write a statement that best describes the position of line segment A B AIR 2 The image shown will undergo a dilation centered at point B with a scale factor of 2 Which lines will not be changed by the transformation tornan ed H 3 In the coordinate plane quadrilateral ABCD has vertices A 1 1 B 5 1 C 5 9 and D 1 9 Quadrilateral FGHJ is shown in the coordinate plane to the right What are the scale factor and the center of dilation that map quadrilateral ABCD onto quadrilateral FGHJ AUCH 35 BOK U B 9 10 4 Under a dilation where the center of dilation is the origin the image of X 3 4 is X 9 12 What are the coordinates of Y the image of Y 5 0 under the same dilation 171

3 5 l 6 X

11 x 1 X

X Alu x 2 4

X 3 2 4 11 11 x 1 x 7 5 12 3x 5 X

7 93 x 1 5 8 8 3 9 x 3 5 3 9 X x 1

Solve each proportion for the variable round answers to the nearest tenth 9 2 1 X 4 3 11 y 14 21 3 56 6 618

4 7 5 11 X 3 5 3 5 x 2 6 6 7 8 6 x 3

For each rectangle write the ratio of the longer side to the shorter side Simplify if possible 1 70 ft 25 ft 2 12 cm 18 cm 3 36 in 21 In

8 Use the figure to answer the following 2 points a What is the measure of the shortest side of the sail on the model Round your answer to the nearest tenth b What is the measure of the longest side Round your answer to the nearest tenth B MAM 9 What is the area of the given triangle Round to the 10 A local park is located on a triangular piece of land nearest tenth 1 point What is the area of the park to the nearest tenth 1 point A 13 cm 7 cm 38 C R 75 m E60 40 28 in 150 m Checkpoint Score Total 11 15

HW 1 What is the ratio equivalent of sin C 34 A C 30 28 Complete problems 1 8 below for independent practice 40 3 What is the ratio equivalent of cos A Hint use the Pythagorean theorem to find the missing side B 8 m When you are finished check the solutions with your teacher 21 16 5 The diagram below represents a ladder leaning on the side of a wall The ladder is 28ft long and the height of the wall reaches 21ft What is the angle between the ladder and the ground 96 B 9 A 7 Find the area of the following triangle 7 m 2 What is the ratio equivalent of cos Z 36 39 35 0 B 4 What is the ratio equivalent of tan C Hint use the Pythagorean theorem to find the missing side 28 139 Y 15 Z A 6 Create a diagram of a ladder leaning on the side of a wall The wall is 16ft tall and the ladder is 18 ft long What is the angle between the ladder and the ground 7 mi 63 8 Find the area of the following triangle 4 mi Optional Complete problems 1 3 5 9 11 from your textbook on separate lined paper When you are finished check the odd problems for solutions at the back of the textbook Grometry A 2020 Page 142

EX 4 y25x 10x 7 Opens Vertex Axis of symmetry x intercepts y intercept vertex Form

3 Write the fraction ratio for each of the following 1 point a tand b sinD c cosD 4 Ifm H 68 what is GI Round your answer to the nearest tenth 1 point 4 8 1 7 G 2 cm F

Lesson 13 3 and 13 4 I can solve right triangle problems using trigonometric ratios and the Pythagorean Theorem 5 Find the measures of the following Round to the nearest whole number 2 points a HT b ZT How I Did Circle one I got it C ZH 15 cm H I m still learning it W 8 cm T

Your Turn 1 A building casts a 33 m shadow when the sun is at an angle of 27 the vertical How tall is the building to the nearest meter How far is it from the top of the building to the tip of the shadow What angle does a ray from the sun along the edge of the shadow make with the ground a Find EF b Find DF c Find m2D DA 2 Use the Pythagorean Theorem to find AB What is the trigonometric ratio equivalent to tan C C 12 B B C OD 12 35 35 12 37 27 11 D133 m E 35 12 37 Shadow 37 Building

b Solve the triangle by finding the length of DF and the measures of all the angles For side lengths round to the nearest tenth For angles round to the nearest degree 2 points a DF LE 2F 7 Find all the missing side lengths for the following triangles 3 points 2 V U 30 5 3 2 60 b 2 2 d b D F 45 a 5 ft E 5 83 ft 7 4 m 45 n

Learning Goal I can solve right triangle problems using trigonometric ratios and the Pythagorean Theorem Standard G SRT 8 EXPLORE Area of Triangles Read Explore passage and complete the activity below Show all your work Example To find the area of a triangle use the following 7 7 km 14 m lem Solving with Trigonometry Area 1 base x height 2 Find the area of the following triangles 8 m 20 7m A bh 16 m 19 km 11 km 1 L4L Student Resource Center http Bit ly LALMath 16 yd 6 yd 11 yd

Trigonometry ASSESSMENT Credit Checkpoint Complete the following problems Show all your work Round all side lengths to the nearest tenth and all degrees to the nearest degree When applicable leave your answers in radical form How I Did Circle one I got it Learning Goal from Lesson 13 1 and 13 2 I can explain how to derive the trigonometric ratios for acute angles 1 Name the following sides of the triangle 1 point a Opposite Leg of ZA b Adjacent Leg to ZA bu A N B 2 Write an equation that can be used to find mzM Then solve it Round to the nearest degree 1 point 5 I m still learning it 11 M

HW 2 1 What values of u and v are correct for the following 45 45 90 right triangle 10 A u 45 D u B C u 10 2 10 6 10 6 v 10 3 u 10 2 v 10 2 v 10 v 10 45 X 11 3 3 Find the missing side lengths Leave your answers as radicals in simplest form m work Complete problems 1 6 below for independent practice 14 When you are finished check the solutions with your teacher 5 Find the missing side lengths Leave your answers as radicals in simplest form 60 y 2 What values of a and b are correct for the following 30 60 90 right triangle 30 A a 34 b 17 3 B a 17 3 b 34 68 3 C a 3 D a 34 b 17 6 4 Find the missing side lengths Leave your answers as radicals in simplest form 16 45 16 17 6 Find the missing side lengths Leave your answers as radicals in simplest form y 30 b 17 6 Optional Complete problems 3 10 18 22 your textbook on separate lined paper

Your Turn Jhangos 1 Find the unknown side lengths and trigonometric ratios for the 45 angles a Find CA b Find AB c Complete the table Angle 45 sinx opp hyp COST adj hyp B 45 tant opp adj 10

1 mzY Love 2 mzz lifelong LEARNING to the nearest degree Geometry A alla staminoghT 23 AOTHAOHO2 14 Credit 5 ZL4L Geometry A 2020 Page 123

B 62 X A 8 C Optional Complete When you

Dik koordinat d zleminde birim ember a a da veri mi tir 1 1 3 olmak zere A m n noktas birim ember zerindedir Buna g re m n arp m n n de eri ka t r M n

Determine is D the two graphs are equivalent E B F 0

1 25p x A 50 cm C 70 B c the amount of change in plate thickness d the final volume of the plate 150 MPa E 70 GPa v 1 3 40 cm 1 5 cm ABC triangle is drawn on the thin plate in the figure when it is unloaded AB length is parallel to the x axis and measured as AB 20cm Determine a the final length of side BC b the amount of change of side AC 90 K MPa

3 Run of mine ore is blended using a stockpile with a conical shape see image below The stockpile has a slope angle of 39 degrees and a height equal to 20 24 m The volume of the stockpile is known to be 13 250 m 39 For calculations relating to this shape recall that the volume V of a cone follows from V R H 20 44 where V is the volume R is the radius of the base H is the height The surface area S of a cone is given by S R RL where S is the surface area R is the radius of the base L is the slant height which is measured along the sloping side a Determine the radius R of the stockpile in m to 2 decimal places b Determine the slant height L in m to 1 decimal place R c Determine the surface area S in m to 0 decimal places To increase the size of the stockpile is adjusted as follows slant height L is increased to 35 m and 0 surface area S increases to 5000 m at the same time while height H remains as before d Determine the new radius R in m to 2 decimal places e Determine the new slope angle in degrees to 1 decimal place Determine the new volume V in m to 0 decimal places 2 marks 2 marks 2 marks 3 marks 2 marks 1 mark