2D Geometry Questions and Answers

14 Regular Quadrilateral 15 Regular Octagon 16

In 11 16 For each regular polygon calculate the measure of 11 12 each angle 13

A Number of sides Name Polygon Number of Triangles Sum of Interior Angles 5 A Number of sides Name Polygon Number of Triangles Sum of Interior Angles 6 Number of sides A Name Polygon Number of Triangles Sum of Interior Angles

In 11 16 For each regular polygon calculate the measure of each angle 11 12 14 Regular Quadrilateral 15 Regular Octagon 13 16 Regular 18 gon

In 7 10 Calculate the sum of the interior angle measures of each polygon 9 15 gon 7 nonagon 8 dodecagon 10 30 sided polygon

6 C 13 7 X 6 12

The Leaning Tower of Pisa currently leans at a 4 angle from vertical and has a vertical height of 55 86 meters What is the length of the tower D A surveyor 30 m from a boathouse sights a cabin at an angle of 59 degrees The distance from the cabin to the boathouse is perpendicular to the distance from the surveyor to the boat house Find the distance from the boathouse to the cabin

7 8 in 8 Find w and x 13 m 48 W 6 m

Use the appropriate trigonometric function to find the value of x in each triangle round sides to the nearest tenth and angles to the nearest degree Don t forget units 3 4 11 A X 40 43 in 55 in

11 A forest ranger in a tower sights a fire 180 meters away If the ranger is 50 meters above the ground find the angle of depression to the fire 50 m 180 m

2 21 52

9 10 m X 56 10 Find w and x 4 32 10 ft 8 ft

16 A 20 ft tree casts a shadow that is 12 ft long Find the angle of elevation of the sun at that time

9 in 6 in X 5 41 11 ft

1 In the diagram above of AJKL JL 7 KL 2 Determine the following ratios Write your answers in simplest radical form sin L ran cos L sin K

38 A Sin H X 14

2 16 16 54

Given m AOB 42 m EOF 66 Prove m COD 72 B E menu Complete the proof It is given that m AOB 42 and m EOF 66 By the m BOC 8 m AOC 108 and by the 66 By the m AOC m COD 180 After application of the B ZEOF ZBOC T Bm COD 72

In circle W m VWU 107 Solve for a if mVU W 3x 39 If necessary round your answer to the nearest tent

4 Let f x arcsinx g x arccos x and h x arctan r Which of these functions is graphed here Explain how you know 3TT 24 TT TT 2 0 TT 2 X

Question 8 A spherical shaped ball that has a radius of 4 inches is currently deflated How much air would it take to completely inflate the ball 512 in A C D 64 in 2048 in T 3 256 3

4 inches Find the volume of one paper cone if the diameter is 4 inches and the height is 7 inches Rour your answer to the nearest cubic incl 29 in 59 in 88 in 117 in A B C 7 inches D

Triangle QRS has a perimeter of 55 If RT bisects angle R what is the length of QT Q A 10 B 12 C 15 R 18 T 12 S

M 50 NK N MK 24 JL 20 L NL ML JM

GE 8 25 10 tan 0 38 A 9 42 O tan 19 35 39 00 35 18 40 64 Sin 9 72 0 72 25

27 A a daki O merkezli emberin ap 3 cm dir AC ve BD kiri leri E noktas nda kesi mekte ve m CEB a dir O 18 2 2 E 8 C AB DC 2 cm oldu una g re cosa ka t r A C 1 1 D E 5 9

14 12 The method developed in Problem 14 11 was used for the routine determination of iron in 25 0 ml aliquots of groundwater Express the concentration as ppm Fe in samples that yielded the accompanying absorbance data 1 00 cm cell Calculate the relative standard deviation of the result Repeat the calculation assuming the absorbance data are means of three measurements c 0 068 e 1 512 d 1 009 f 0 546 a 0 143 b 0 675

14 11 A standard solution was put through appropriate dilutions to give the concentrations of iron shown next The iron 11 1 10 phenanthroline complex was then formed in 25 0 mL aliquots of these solutions following which each was diluted to 50 0 mL The following absorbances 1 00 cm cells were recorded at 510 nm Fe II Concentration in Original Solutions ppm 4 00 10 0 16 0 24 0 32 0 A510 0 160 0 390 0 630 0 950 1 260

13 11 The equilibrium constant for the conjugate acid base pair HIn H OH 0 In is 8 00 x 105 From the additional information in the following table a calculate the absorbance at 430 nm and 600 nm for the following indicator concentrations 3 00 10 M 2 00 10 M 1 00 10 M 0 500 10 M and 0 250 10 4 M b plot absorbance as a function of indicator concentration Species HIn In Absorption Maximum nm 430 600 Molar Absorptivity 430 nm 8 04 10 0 775 X 10 600 nm 1 23 x 10 6 96 10

Fill in the following table by writing the formulas for the perimeter and circumference of the given shapes and finding each shape s actual perimeter or circumference 7cm One sticlan 4cm Shape Polygons 3cm 4cm 11cm Circle 12 in 3cm 3cm 9 7cm Formula 2 AB AH 2 EF FG 4 CD 201 2 7 4 267 3 4 4 2 4 Testfemur sin 722 20 16 8 500m 2 TT 2TTX12 Trova 75 39 inch istorana Actual

Lesson 19 3 Homework HW Complete problems 1 6 below for independ 1 Find the surface area of the regular pyramid below A 7 in 15 ft 6 9 in 12 km When you are finished check the solutions in the back of the t 7 in 3 Find the surface area of the regular pyramid below 10 ft 5 Find the surface area of the cone below 26 8 km 2 Find the surface area of the regular pyramid below 11 mm 8 mm 8 mm 4 Find the surface area of the cone below 13 4 km 6 km 6 Find the surface area of the cone below 8 in 9 8 in Optional Complete problems 5 6 8 9 11 12 from your textbook on separate lined paper for extra pract When you are finished check the odd proble

The surface Your Turn Each aluminum can is a right cylinder Find the total amount of aluminum needed to make the can Leave your answer in terms of 1 15 cm 6 cm 2 Pas 80 mm 72 mm

5 Find the volume of the cone below 10 cm La 10 cm 6 Find the volume of a cone that has a height of 9 inches and a diameter of 12 inches Use 3 14 for and round to the nearest tenth 7 Find the volume of the composite figure Use 3 14 for 7 and round to the nearest tenth The dimensions of the cylindrical conical tank are as follows The radius of the cylinder and cone 17 inches Height of the cylinder 50 inches Height of the cone 32 inches The volume of the cylinder and the cone is given Show the work necessary to find the volume of the composite figure a Show the work to find the volume of the cylinder is V 45373 in b Show the work to find the volume of the cone is V 9679 6 in c Use what you know about composite figures to estimate the volume of the cylindrical conical tank Optional Complete problems 2 5 7 9 10 15 23 from your textbook on separate lined paper for extra practice When you are finished check the odd problems for solutions at the back of the fouthal

shapes 7cm 4cm Shape Polygons 3cm 3cm 4cm 11cm Circle 12 in 3cm 7cm Formula One sticky note is a two dimensional shape like all the previous shapes Describe or draw the shape you would get if you took a lot of sticky notes and stacked them perfectly on top of each other In this credit you will be learning about three dimensional shapes which are created by stacking many two dimensional shapes on top of each other like sticky notes Thinking about how a three dimensional shape is made may help you throughout the credit

Find the volume of each pyramid 1 A piece of pure silver in the shape of a rectangular pyramid has the dimensions shown below What is the volume of this piece of pure silver 2 5 cm 1 5 cm 1 5 cm

Given NQ is the bisector of LMNP and ZNMQ ZNPQ Prove A MNQAPNQ M N Q P

S 70 T U 220 V 19 from your textbook on separate lined paper blems for solutions at the back of the textbook

Lesson 16 2 Checkpoint Once you have completed the above problems and checked your solutions compl below Complete the Lesson Reflection above by circling your current understanding of t For 1 2 use 3 14 for mr Round to the nearest tenth 1 Find the arc length of minor arc AB 3 in 120 B LABC is a central angle in a circle with center B The length of the radius is 13 km and mzABC 45 What is the length of minor arc AC hint create your own diagram

Turn ert each angle measure to its equivalent radian measure Leave your answers in terms of 90 5

APS ST

6 10 in Y 133 17 in Z

20 279 Round answers to nearest whole number

45 6

20 X 13 on to the given blank paper 2 Round answers to nearest whole number X 39

20 fi 15 A 36 116 S T ZR Area

10 Given AABC has the following coordinates A 0 5 B 2 1 C 2 3 Perform the following transformations 1 Translate AABC along the vector 5 7 A B 2 Dilate AA B C by a scale factor of k from a Center of Dilation of 3 2 B A C C

Your Turn Find the unknown arc measure 1 mKLN M 48 K Q 86 79 N

Your Turn Find the measures using the figure provided 1 mPN 2 m2MNP 61 N 238 M

An equilateral triangle is inscribed in a circle Use your knowledge of equilateral triangles to strengthen your understanding of inscribed angles and their arcs You may describe or demonstrate your knowledge of the Inscribed Angle Theorem with an equilateral triangle inscribed in a circle Optional Complete problems 1 5 13 21 24 from your textbook on separate lined paper for extra practice When you are finished check the odd problems for solutions at the back of the textbook

The circumference of a tree is Use 3 14 for m 2 The circumference of a circular fountain is 32 feet What is its diameter Round to the nearest tenth of a foot Use 3 14 for m