Solution of triangles Questions and Answers

In the figure below g o Find the values of x and y g m 70 3y 26 x O X y

perpendicular directions to chase their Pokemon Figure A shows their paths and the locations where they each catch a Pokemon Note The small squares in the grid have side lengths of one yard and areas of 1 square yar Figure A Dolores start 7 Marianne The red vertical line represents the path Dolores walked How far did Dolores walk before she caught a Pokemon yards The blue horizontal line represents the path Marianne walked How far did Marianne walk before she caught a Pokemon What is the distance between the spot wh yards

10 Dikd rtgen eklindeki bir ka t zerine krokisi izilmi olan bir nehrin izledi i yolun yapt a lar ekildeki gibidir Nehrin izledi i yolun kar l kl kenarlan pa ralel oldu una g re m BCD a ka derecedir SO C168 RA 70 PB N 35 D 77 100 M D K F 150 a 28 E you F 80

Determine the angle in the design of the streetlight shown in the figure where x 2 1 Round your answer to one decimal place 0 127 2

nd all points if any of horizontal and vertical tangency to the portion of the curve shown Enter your answers as a comma separated x cos 0 8 sin y sin 0 0 cos 0 2n 50 2 horizontal tangents vertical tangents 8 0 468 xx

6 Assume angle B is a right angle Label the point where the altitude intersects the hypotenuse D If segment AD is 3 less than 3 times the length of segment DC and the altitude of the triangle is 6 find the length of segment AD Show your work and round to the nearest tenth B

and m P 72 x then the value of x determine I P Q

A SAS 3 ASA C HL D SAA A D congruent Overlapping Triangles

The medians of AABC are AE BF and CD They meet at a single point G In other words G is the centroid of AABC Suppose GF 8 GD 4 and AE 33 Find the following lengths Note that the figure is not drawn to scale O F B E C CD AG BG 010 X

nonument outside city hall has dimensions as shown in the figure below If one gallon of paint can cover 203 ft how many gallons of paint must be bought in er to paint the monument Assume that the base of the monument cannot be painted and that paint can be bought only by the gallon 15 ft 10 ft 36 ft 15 ft gallons X

For triangle DEF given sides d 38 e 42 and f 47 Find measure of angle F Your answer will be numerical only and round to the nearest tenth

Question 0 Provide your answer below 47 in a A carpenter needs to cut a small triangular piece of wood for part of a jewelry box He knows the dimension shown and that 0 38 What is the length of a to the nearest tenth of an inch Do not include the units in your answer

A hiker is standing on the ground looking up to the top of a tree with an angle of elevation of 0 55 The situation is represented where the base of the triangle is the eye level of the hiker and the vertical side is the tree The distance from the hiker s eye to the top of the tree is 54 feet Based on the information given what is the distance a in feet from the hiker to the base of the tree Do not include the units in your answer Round to the nearest whole number Provide your

PQ RQ and PS RS px a 160 90 b R

Given the triangle Enter an exact answer in fraction form 0 15 17 8

Question 41 Points 1 Identify the volume of a sphere with a diameter of 6 inches O 36 t in 48 in 216 in 288 in

15 20 37 Use the Pythagorean Theorem to set up an equation to solve for x 38 Solve forx O 14 O 5 13 Ox 5 5 Ox 25

Question 3 Find the missing angle of VOW from the given figure 19 O 61 O 66 Points O 96 W

Question 1 What is the value of O 0 3535 O 0 65 Points 1 O 0 125 O 0 75 sin45 2

The side measures of the triangle are 4 cm 7 cm and 9 cm Find the perimeter of the triangle 20 cm 252 cm 25 cm Points 3 18 cm

Which of the following can be used to find the volume V of a sphere whose radius is r O V 4 3T cubic units V 2 3 r cubic units O V 4r cubic units

30 sing 9 sn 9 3 Jan T 2 3cos x ilerden hangisine e ittir B 2 sin x D 1 cos x 2007 2sin x cos x cos x t 2 COS 6 sin 28 co a 2 3 6 ng sin x sinx cos x cos3x cosx sin2x D tan x B cos x 1 02 0 ifadesinin sadele tirilmi bi imi a a dakiler den hangisidir A sinx 1 sin 2x E 1 18 col C cotx 9 2sin 8 cos e cos 0 3sin E oldu una g re cot 0 k B 1 3 A 2 D 10 1 C2 D 3

8 Which trigonometric ratio could we use with the given information to find 9 Find 15 A 150 11 Find y x Round to two decimal places 10 Which trigonometric ratio could we use with the given information to find y

From A to B a private plane flies 2 9 hours at 110 mph on a bearing of 69 It turns at point B and continue another 2 1 hours at the same speed but on a bearing of 159 to point C Round each answer to three decimal places At the end of this time how far is the plane from its starting point On what bearing is the plane from its original location degrees miles

Given the following parametric equation eliminate the parameter to get an equation involving just x and y x 2 cost 1 y 5 sint O Be careful here Check your signs 1 x 1 y 4 25 for n t 2 1 x 2 y 5 1 z 1 1 2 None of these x 2 y 5 1 z 1 2 1 y 25 4 z 1 3 1 2 5

16 In AABC M and N are the midpoints of AB and BC respectively MN x 5 AC x 2x 5 Find x MN A 2 points C M N B

4 Given m BCD 7 x 4 m A 2 2x 5 and m B 2 3x 1 Find x m BCD 2 points A B C

A certain ladder is 61 feet long and is leaning against a house If the ladder is 6 feet from the base of a house find the height from the base of the house to the top of the ladder 5 What is the length of the Hypotenuse the longest side C Hypotenuse r ft Use the button to input your answer 6 Use the Pythagorean Theorem to set up an equation to solve for the missing side x i Use the button to input your answer

Which of the following identities from the list below is an odd even identity Select one a csc 0 cscf O b tanecot 0 OC cost sinA seco cosl

21 Find the exact perimeter and area of the segment shown given that mo 60 and OA 12 in Exercises 21 22 A B

1 Draw the angle bisector on the triangle from vertex A O O O B B B C OPTIO

11 The lengths of sides of the triangular base are a 4 cm b 5 cm and c 7 cm s s aXs bs c to find the area of the triangle Use the Heron s Formula A a b c 2 b 2 points a

1 Suppose we want to solve the cubic x Ax Bx C 0 To use our algorithm we make the substitution x u A 3 to get a cubic polynomial in u that has no square term This is called completing the cube We then use our algorithm to solve this cubic by using a circle centered at a b Solve for a and b in terms of A B and C 2 The length 2 cos 2 13 is a root of p x x ax x a 1 where a is the larger root of q x x x 3 What center a b should we use to solve the cubic Note that the center is constructible using

12 This shape is BEST described as being a n 13 Based on this type of triangle we know that y 14 Since the perpendicular bisector splits this into to two A s we can set up the folla x 80 X X 180 15 Find the measures of x and y y 180 degrees degrees

2 This shape is BEST described as being a n 3 Based on this type of triangle we know that x 4 Set up an equation to solve for the missing angles x y 40 x y 5 Find the measures of x and y X y degrees degrees

X 11 Find x X 12 Find y y 13 Find z Z N 70 60 degrees degrees degrees

x 2 A x3x 2x 4 Angle B x 3x C 7 Since B is split by a line we must add the two parts of the angle together 8 Set up an equation to solve for x x 2 2x 4 Input your answers WITHOUT spaces

c csc2 x 2csc x cot x cot2 x tan2 x N X 3 points

For each pair of triangles determine whether the Hypotenuse Leg HL Congruence Property can be used to prove that the triangles are congruent If necessary you may learn what the markings on a figure indicate Can the HL Congruence Property be used Can the HL Congruence Property be used a 47 28 m Yes Yes O No O No 28 m b d O Yes Yes O No JD X O No

Do the figures below have rotational symmetry Point symmetry If a figure has rotational symmetry give the smallest angle of rotation needed for the figure to appear unmoved Rotational symmetry Yes No Angle Point symmetry Yes No O Rotational symmetry Yes No Angle Point symmetry Yes O No X

Use the given information to prove that ARST AUVT Given RST is a right angle ZUVTIS a right angle 1 2 3 4 5 6 U Statement ZRST is a right angle ZUVT is a right angle RST LUVT ST RTS ARST AUVT ST a VT Prove ARST AUFT Reason Given Given Reason 7 Given Vertical Angles Property Reason 2

3 Express each of the following as a single trig ratio and then evaluate I 2sin cos I

2 Given DV 1 TU Is ADVT ADVU T D V U

Karamjit makes sure that every employee is recognized on their birthday The staff will gather for a catered lunch During the lunch Karamjit will recognize the employee and praise their accomplishments to everyone This is an example of Responsible Leadership Story Ceremony Ritual Coalition

Find the equation of the line passing through 3 0 and perpendicular to the line y 7x 3 O y 1 7 x 3 O y 1 7 x 3 O y 7 x 3 O y 1 7 x 3

ger brother has challenged you to a swimming race to see who can swim to the opposite side of the pool first You know that your brother swims slower than you so to make things even you choose to swim along a path at a 40 degree angle from the path that would go directly across the pool as shown in the diagram The pool is 60 ft wide 8 points B your path 40 brother s path 60 ft C 1 How long is the linear path you chose to follow 2 If your brother swims directly across the pool how far apart will you be when you both get to the other side

Question 3 Points 1 Find the equation of a circle whose center is at 2 3 and radius is 3 units O x 2 y 3 9 O x 2 y 3 9 O x 2 y 3 9 O x 2 y 3 9

Establish the identity cot B cot a cot 1 cot cot a

N B the Midpoint of LO PO 8 IN AOPN Paragraph to establish the Proof P All changes save 5 We know that N is the Midpoint of LO and LM PO because the information is 6 Therefore we can establish that LN ON because of the 7 We can also establish that MP because of they are 8 We can also establish that LO because of they are also 9 Using all of this information together we can prove that ALMN AOPN by

4 Given AABC M and N are the midpoints of AC and BC respectively Prove AMNC AABC Proof Statements 1 AABC M and N are the midpoints of AC and BC 2 MN AB 3 ZCMNZA ZCNM ZB 4 AMNC AABC 3 points 1 2 3 4 A M C Reasons N B