2D Geometry Questions and Answers

The center of the circle is C Find each measure using the appropriate theorems and postulates 1 m MLP 70 M 60 CN Elaborate 2 Select which statements are true or false in this figure using the theorems you learned in this lesson There are three true statements

5 A blimp that is filming a football game makes a 7 angle of depression to the stadium If the blimp s altitude is 400 m find the line of sight distance from the blimp to the stadium

A surveyor is looking up at the top of a building that is 140 meters tall His eye level is 1 4 mete angle from his eyes to the top of the building above the ground and he is standing 190 meters from the building Calculate the measure of the 140 m 8 A hot 190 m ta XI 1 4 m

3 Find the arc length of BC O B B 56 4 Find the measure of ZD felong C 50 C 134 OP WAS HAZME

8 A hot air balloon lifts 125 feet into the air The diagram below shows that the hot air balloon was blown to the side How long is the piece of rope that connects the balloon to the ground 9 x 1 4 m 125 ft

or is looking up at the top of a building that is 140 meters tall His eye level is 1 4 meters above the ground and he is standing 190 meters from the building Calculate the measure of the angle from his eyes to the top of the building 140 m 190 m ta 1 4 m www

1 m MPK 2 MPE 61 M 127 D O 134 111

Your Turn Determine the unknown values in each figure 1 117 h 2 4 m CDA 45 Elaborate Problems 3 6 requires you to apply your knowledge from Lessons 15 1 through 15 3 Refer to the figure for Problems 3 6 AB is tangent to OC at point B and AD is tangent to OC at point D Determine the angle measures 3 m BCD 5 m BED 6 m DBA N 5 32 B

1 Reflect Both lines in the figure are tangent to the circle and AB is a diameter What can you conclude about the tangent lines

HW Complete problems 1 7 for independent practice Find the measure of the arc or central angle for the following circles 1 Find the measure of ZRQS R S D Use the Inscribed Angle Theorem to find missing angle measures 2 Find the measure of ZD 124 3 Find the arc length of BC 4 Find the measure of LD When you are finished check the solutions with your teach 134

Lesson 15 4 Checkpoint Once you have completed the above problems and checked your solutions complete the Le below Complete the Lesson Reflection above by circling your current understanding of the Learni 1 Find the value of x and J M 6 X N L H K 10 2 Find the value of y and the length of each secant segment y 18 7 N J 10 M 9 L

HW Complete problems 1 4 below for independent practice When you are finished check the solutions with your teacher For 1 and 2 use the figure on the right LK and LM are tangent to the circle Both KJ and MJ connect to the center of the circle at point J K 1 What is the measurement of ZKJM 2 What is the measurement of ZLMJ 60 4 What is the measurement of LADC and LABC L For 3 and 4 use the figure on the right CB and CD are tangent to the circle Both BA and DA connect to the center of the circle at point A 3 What is the measurement of BCD M B 127 G Optional Complete problems 4 8 13 16 18 19 from your textbook on separate lined paper for extra practice

1 Find the value of x Round the answer to the nearest tenth or leave it in radical form 6 O B 4 X C 2 On a bird watching trip you travel along a path tangent to a circular pond to lookout station that faces a hawk s nest Given the measurements in the diagram on your bird watching map how far is the nest from the lookout station Nest X 25yd Lookout Station 100yd Path

Critiquing Your Friend s Work Your friend was asked to solve for the value of y using secant secant product theorem but solved for it incorrectly Help your friend by explaining or demonstrating how to solve for y correctly 2 Solve for y Your Friend s Work HL JL NL ML y 10 27 9 10y 243 y 24 3 y 24 3 Your Work N H y 18 J 10 M 9

Your Turn Find the measure of the arc for the following circles 1 Find the measure of RS OF O 2 Find mBD If mEF 45 and mZACD 56 determine mBD using the appropriate theorems and postulates AE BF and DC intersect at Point C 3 Find the value of x 4x 21 VAW 78

Try This For the given image name the 2 tangent lines and the points of tangency For the given image name the 2 tangent lines and the 3 points of tangency Tangent lines Points of tangency EXPLAIN 1 Proving the Tangent Radius Theorem Read the section below and complete the following activity adapted from Lesson 15 3 Tangent Radius Theorem If a line is tangent to a circle then it is perpendicular to a radius drawn to the point of tangency C

Checkpoint Once you have completed the above problems and checked your solutions complete t below Complete the Lesson Reflection above by circling your current understanding of the L 1 Find the value of x given m2SAR 7x 7 and mzSQR 9x 7 e 9x 17 7x 7 R S 9x 7 2 Find the value of x Then find the measure of RQ mRP 9x 17 mfQ 6x 1Z meRPQ 5x 15 Given Sr 15 R 6x 12

156 Slope run Reminder The slope of a line is how steep it is It is calculated as the ratio of Start at the bottom left corner of the graph paper and make a staircase with the indicated rise anc run Then draw a line touching the tips of each stair A rise 1 run 1 slope of 1 C rise 2 run 1 slope of 2 B rise 3 run 2 3 slope of 2 D rise 1 run 2 slope of

In 1 2 label each angle as an elevation or a depression 1 a Ll b 42 C 23 d 24 Refit 3 2 2 a Zl b 22 C 23 d 24

4 The horizontal distance from a person to a kite is 85 ft and 100 ft of string has been let out Use the diagram below to find the angle of elevation from the person to the kite 100 ft 85 ft

Flat Tax Some Americans are supporting switching to a flat income tax rate of 15 How much would you pay under this plan Your Income X 15 or 15 Calculator Tip To multiply by a percentage you can use your calculator in two ways You can use the percent symbol key or you can enter the percentage as a decimal To change a percentage to a decimal move the decimal point two digit places to the left Example 20 becomes 0 20 Regressive Tax Plan Mark X next to the row that matches your yearly income TOTAL Proposed Regressive Plan 40 on income up to 25 000 30 on income between 25 000 and 34 000 25 on income between 34 000 and 44 000 20 on income between 44 000 and 80 000 10 on taxable income over 80 000 Calculate your tax For example 10 000x40 4 000 in tax

2 Find the sine cosine and tangent for ZB 26 10 B 3 Find the sine cosine and tangent for ZC 20

Use the appropriate trigonometric function to find the value of of x in each triangle round sides to the nearest tenth and angles to the nearest degree Don t forget units 4 5 9 in 6 in x 41th 11 ft 6 64 m 31 m X

7 yd 8 10 m 56 9 Find w and x 32 W 10 ft 8 ft

1 Complete using hypotenuse opposite and adjacent In Sin A Cos A Tan A A Sin A Cos A Tan TII

4 a a go 30 b 10 b 5 a b 30 a 4 5 b 60 answer must be in simple r 6 X 12 30 x y 6

4 3 2 1 V 24 2 3 2 3 What is the slope of the line

find the value of x 56 50 n

3 7 17

7 16 20 X 8 x 12 5 15 9 9

X 70 y 15 yd

2 9 cm E ale trig function to find the value of x and y round answers to the nearest tenth Geometry Worksheet 8 2B X 7 13 in y 3 y 5 m Cos A Tan A

8 The graph of y A cos x C D is shown for some constants A C and D Find the values of A C and D 2 V TT 2 TT 2 3TT 2 2TT N 1 2

10 Write two equations for the graph shown one using sine and one using cosine TT TT 2 3 2 1 0 T 2 TT 3TV2 2TT

6 The graph of y cosa is reflected across the y axis and horizontally stretched by the factor of following is affected A Range B Amplitude C Period D Domain 113 Which of the

A scientist is studying how an antibiotic affects a bacteria colony The colony has a population of 20 000 when she applies the antibiotic Each hour after the application the population of the colony is of its size from the previous hour Let P be the size of the colony r hours after the scientist applies the antibiotic Which equation is an explicit formula for P in terms of r A P 20 000 t B P 20 000 2 C P 20 000 1 D P 20 000 5

7 20 m 530 8 75 30 ft 9 16 yd 15

4 12 cm 620 X 5 70 7 in X 6 X 13 ft 32

Amy is helping plan her school s new basketball court The west edge of the basketball court is located on the line y 5x 2 The east edge cannot intersect with the west edge On which line could the east edge be located O y 5x 100 y 5x 100 O 5x y 50 O 5x y 50

answers need to be in simplest radical form In 1 2 Find the sine cosine and tangent ratios for ZA in each t 1 2 2 3 B 2 A

In 3 4 Find the sine cosine and tangent ratios for ZM in each triangle 4 3 L 33 K 7 4 M K 22 M 16

8 Find the sine cosine and tangent for 60 6 30 4 3 2 3 60

4 Here is parallelogram ABCD A M D Prove segment AM is congruent to segment CM

5 Could this be the graph of y not sin x Why or why AN

cos 3 x sin 2x x sin x x sin 2x x sin x cos x Some trigonometric expressions are written in the squares given in the figure Which of the following figures can be obtained by combining four equal expressions

The lengths for the sides of a triangle are given Classify each triangle as acute rig 14 3 3 4 15 15 12 9

In 8 11 Use Pythagorean s Theorem to find the value of the variable Answers should be in simplest radical form drawings are not to scale 8 3 2 in 7 5 in X 9 10 cm 14 cm X

n 16 19 Find the value of each variable Answers should be in simplest radical form 5 17 45 X 459 14 X 45 24 45

n 6 7 Rationalize the denominator answer in simplest radical form 3 5 7 6 14

12 List the sides for the triangle in order from shortest to longest drawing is not to scale D 56 The lengths for the sides of a frin 13 List the angles for the triangle in order from smallest to greatest drawing is not to scale 5 9 in 8 2 in 5 2 in B