Solution of triangles Questions and Answers

1 6pts Using the figure below find the measures of the following angles in degrees a What is the m ABC b What is the m BCA c What is the m CAB A 2x 5

Compare m ABD and m BDC A 21 B O mzABD mzBDC O mzABD mzBDC OmzABD mzBDC 20 D

In Exercises 4 6 find the value of x 4 30 X 40 5

Solve for m N N 6 W 24 Angle N

In AGHI GH JK Given that IG 35 GH 49 and JK 21 find IJ G J K H IJ 0 X

For the following exercises find the lengths of the missing sides if side a is opposite angle A side b is opposite angle B and side c is the hypotenuse 10 cos B a 10 11 sin B a 20 12 tan A 5 6 6 13 tan A 100 b 100 14 sin B 3 2 15 a 5 4 A 60

In the figure below I II m X 0 135 xo X Find x 39 m

Which equation can we use to find the length of the side labeled x 5 A sin 30 B cos 30 c tan 30 D sin 30 20 88 10 20 88 10 5 5 5 30

A 12 foot ladder that is leaning against a wall makes a 75 5 angle with the level ground Which of the following equations can be used to determine the height y above the ground in feet that the ladder touches the wall A cos 75 5 B sin 75 5 C cos 75 5 D sin 75 5 12 12 Y 12 Y Y 12

Given m ZELG 124 Prove x 28 D 2x H G E F Complete the steps in the two column proof 1 mZELG 124 Statements 2 mZELD 2x 3 ZELG and ZELD are a linear pair 4 mZELD mZELG 180 5 2x 124180 6 7 x 28 Reasons 1 given 2 given 3 definition of a linear pai 4 4 5 substitution 6 subtraction property 7 division property

12 Given CDEF S and T are the midpoints of EF and ED Prove SR FD C F S D T R

a Using a trig identity write x t 3 cos 7t 2 sin 7t using only one cosine function x t sqrt 13 cos 7t 146 3099 b Using a trig identity write x t 3 cos 7t 2 sin 7t using only one cosine function x t sqrt 13 cos 7t 33 69006753 help formulas x t e 5t sqrt 13 cos 7t 146 3099 help formulas c Using a trig identity write x t e 5t 3 cos 7t 2 sin 7t using only one cosine function in your answer help formulas

O O O U O 3X 6 S x 1 P P by the Reflex Prop of Since TO US PTO PUS by the Corr s Post Therefore A PTO NA PUS by AA TO 15 and US 6 www ZUZS Since TO US ZPTO ZPUS by the Alt Int Zs Thm Therefore A PTONA PUS by AA TO 15 and US 6 ZU ZS Since TOUS PTO PUS by the Alt Int s Thm Therefore A PTO A PUS by AA TO 6 and US 15 P P by the Reflex Prop of Since TO US ZPTOPUS by the Corr s Post Therefore APTO A PUS by AA n TO

AABC is congruent to ADEF Find x and then m CAB and m FDE A C 3x 3 X m CAB COD F E Note Always make sure the value of a produces positive angles O B O D 4x 11

Health Plan Comparison Plan 1 Plan 2 How much money 1 000 00 3 000 00 can you expect to 30 00 0 00 owe for an Deductible Office Visit cost Monthly Premium Individual emergency room 70 00 35 00 visit under Plan 2 Individual Family 1 100 00 1 200 00 A 35 00 B 3 000 00 C 0 D 1 000 00

R Question 4 25 Question 5 2 pts Find the length of PS to the nearest hundredth Type your answer as a number only Example 10 not PS 10 2 pts Find the length of RQ Type your answer as a number only Example 10 not RQ 10

2 Find the m 1 and m 2 in the picture below m 1 m 2 1 146 2

M P L N Line segment ON is perpendicular to line segment ML Line segment OM 17 units in length line segment PN 3 units in length What is the length of chor Round your answer to the nearest hundredth Type your answer

12 x y 14 x y 16 x y Z X 30 24 2 45 y N y 45 6 7 60 y

Angle B is an acute angle in a right triangle What is a reasonable approximation for angle B if the ratio for the opposite leg divided by the hypotenuse is 0 67 not using sine or cosine symbols just geometry

Q P 80 8 cm R What fraction of the interior of the circle is shaded Simplify your answer Which expression represents the area of the shaded sector in square centimeters 16 Z 16 64x 64 8

Given ABCD is a parallelogram with AB 12cm BC 17cm AE 10cm B 17 cm C 12 cm 10 cm E A D What is the perimeter of triangle ADC Keypad

Show that the volume of the prism can be given by 18x 2 6x 3 cm 3 by substituting y 9 3x

Given the right triangles in the figure select the answer that provides the length of the side ED A 2 8 m 2 1 m 5 833 m E 3 5 m D 6 m B 8 m C

Isosceles triangle ABC contains angle bisectors BF AD and CE that intersect at X A 46 67 115 E If BA BC and mzBCA 46 what is mzCXA 134 B F X D C

Given AMNO find the measure of LMN L 38 52 76 104 M N 104 P

Solve the right triangle ABC with C 90 B 69 2 b 124 in A a C Simplify your answer Type an integer or a decimal Round to the nearest tenth as needee in Simplify your answer Type an integer or a decimal Round to the nearest tenth as neede in Simplify your answer Type a whole number

5 In the diagram AABC ADEF mzB 75 and m2D 30 What type of triangle is triangle ABC Corresponding angles of similar triangles are congruent 6 In the diagram above AABC ADEF and AB 4 feet DE 2 feet BC 4x2 feet and FE 3x 2 feet What is the length of BC B C

cy Part 1 of 4 raw a Venn diagram and use the given information to fill the number of elements for each region A 33 n B 29 n AUB 47 n ANB 13 egion 1 has elements

List all congruent sides and circle the congruence DETERMINTNG CONGRUENCE Decide whe true Eaptain your regsoning xy

15 R Given T wal S E Angle S is a right angle ED I RT Prove DR X TS ED SR

es I and mare parallel lines cut by the transversal line t Which THREE angles are congruent to 5 A 22 B 21 5 6 7 8 C 26

Siven that lines a and b are parallel what angles formed on line b when cut by the transversal are congruent with 23 A B C D 26 and 28 E 25 and 27 27 and 28 26 and 27 5 6 8 25 and 26

7 Determine which two of the three given triangles are similar Find the scale factor for the pair 3 points 33 27 S 7 Show the proportions for all three comparing side lengths Scale factor Which two are similar Triangle Triangle

2 Given ED CA Prove AABC ADBE A E D

a For the following figure the value of a is b 8 in 450 A 8 2in B 16 in 4 2 in 64 am X 45 Part B Using the same figure determine the value of y Choose the suitable option B

ZS and ZSTU are supplementary Complete the proof that ATUV ASRV S 1 R U Statement V T ZS and ZSTU are supplementary ZV ZV m UTV m2STU 180 2 3 4 m s m2STU 180 5 m UTV m2STU m s mZSTU 6 m UTV m S Reason Given Reflexive Property of Congruence Angles forming a linear pair sum to 180 Properties of addition subtraction multiplication and division Ver en espa ol

2 12pts Using Figure 2 below calculate the length of CD CO and EO Round your answers to the nearest hundredth CD CO EO 5 0 O

Determine the length of the missing sides and angles of the triangle given 1 a 10 3 in b 14 5 in and C 54 2 b 12 2 ft c 25 ft and A 34 3 a 7 in B 40 and C 30 4 a 4 m b 7 m and c 9m C B a

1 2 points Prove AABC ADEF Given B LE ZA ZD 2 Steps ZB ZE ZA D AABC ADEF 3 points Prove AABC ADEF Given AB Reasons i Siven ii A4 A C BC DE BC B LE EF Steps AB BC DE EF B LE AABC ADEF B D F E Reasons Diven 1 Ver to iii SAS

perimeter of the composite figure below semicircle Round to the nearest tenth Use 3 14 11 12 1 1 1 1 20

10 NFGH is an isosceles trapezold with diagonals that intersect at point R N H Select all of the statements that must be true A NG FH B NG LFH B

10 B KATX B n taraf pembe arka taraf gri olan ikizkenar gen yu kar da g sterildi i gibi B k esi AC ile ak acak ekilde katlan yor Buna g re m CKB x ka derecedir A 30 B 40 C 50 D 60 E 70

belo answer to the nearest hundredth A 9 B D 10 Figure 1 C AD

Is AABC ADEF Explain BE A HL No C F SAS AAS ASA D Yes are not are

1 y 2 2 Evaluate the integral x y 1 dx along the path ABCDA shown in figure dy xzdz x 2 4 D 0 0 4 B 0 0 0 A 2 0 0 C 0 2 0

4 In each case find the value of the indicated unknown a In AABC find the measure of ZC if ZB 90 a 15 m b 40 m Jeit vihalimiz sv019 x b In AXYZ find the measure of ZZ if x 12 cm y 15 cm z 20 cm

23 The radius of the base of the right circular cone shown below is 2 inches and the slant height is 5 inches Which of the following trigonometric ratios would help you find the measure of the angle 8 A cos8 B sin C O A B 2 5 C D sin sin0 D cos 8 2 5 5 2 2 5 0

1 1 point The angle of elevation to a nearby tree from a point on the ground is measured to be 47 How tall is the tree if the point on the ground is 34 feet from the tree Round your answer to the nearest tenth of a foot if necessary 2 34 Type your answer 1 point From a hot air balloon Addison measures a 27 angle of depression to a landmark that s 989 feet away measuring horizontally What s the balloon s vertical distance above the ground Round your answer to the nearest tenth of a foot if necessary 989 DO 989

Solve the equation Simplify the solution s Use a comma to separate solutions if needed 182 10 Enter the correct value s or expression s in the box I W Hide Hints When solving a quadratic equation first isolate the squared variable on one side of the equation 7 4 1 A 8 5 2 9 6 3 X