Solution of triangles Questions and Answers

Which of the following is not a grouped data sample Select one or more a c b Hair Color Interval Tally Frequency Blonde Brown Black Color Treated Height of Trees Interval Tally Frequency 0 w 20 20 w 50 50 w 80 80 w 110 110 Size of a School Interval 0 S 300 300 S 800 800 S 1500 1500 S 2500 Tally Frequency

1 Iron II oxide Formula Molar Mass

Given M Q QR MN What is the third congruence needed to prove that AMNL AQRP by ASA

iven ZD ZC and ZCAB ZDBA rove AABC ABAD Step 1 Statement ZD ZC ZCAB ZDBA Type of Statement D Reason Given Note AC and DB are segments B

Use a double angle formula to make the required calculation x t 7 tan t 11 Find tan 21 Give an exact answer Use symbolic notation and fractions where needed tan 2

O 60 yd 33 50 yd 57 vards P 33 yd N AONP AVWX What is WX V W

1 Solve for all possible triangles that satisfy the given conditions First sketch the triangle After you re done decide which of the 4 cases above that your triangle falls into a LA 40 b 95 a 40 You ll need a calculator to find the inverse sine

Which expressions represent the length of Please select twe Show your work here 8 25 8 25 cos 31 8 25 sin 59 8 25 cos 59 8 25 sin 31 8 25 sin 31 8 25 8 25 cos 31 C 59 8 25

3 1 1 3 Figure 1 6 15 The graph of y g x a What is the approximate slope of the tangent line to y g x at the point 2 g 2 b How many real number solutions can there be to the equation g x 0 Justify your conclusion fully and carefully by explaining what you know about how the graph of g must behave based on the given graph of g c On the interval 3 3 how many times does the concavity of g change Why d Use the provided graph to estimate the value of g 2

Find an equation of the hyperbola that satisfies the given conditions Vertices 0 3 length of conjugate axis is 8

Find the length of segment WS R 00 8 S W 6x 12x Q 9 P

Solve for x Round to the nearest tenth if necessary 69 I K 40 X J

Triangle K is a scaled copy of triangle J What is the value of m W Write the number only 8 73 28 Triangle J 17 4 14 Triangle K

5 Find all solutions of the equation in the interval 0 27 Write your answer in radian in terms of sinz 3 tanz 3 0

21 Simplify the Radical A 6x 0 10 B 2z 15 C 4x5 15 6z 10 D V60x10

Given the radical equation x 6 x 0 which statement is true regarding the solution to the equation A There are infinitely many solutions to the equation B D There are two solutions to the equation There is one solution to the equation There is no solution to the equation T

4 What are the solutions to the equation 4x4 35x2 9 0 x 3i t A B C D x 91 1 x 3i 2 X 91 2

How do you prove each of the following theorems using either a two columm paragraph or flow chart proof Midsegment of a Triangle Theorem Concurrency of Medians Theorem 4 O How do you use theorems about trianglon to O

Use a trigonometric ratio to solve for a Round to two decimal places as necessary 30 Show your work here 67 a

371 4 1 Convert radians to degrees 57 6 3 Convert radians to degrees 5 Estimate and draw a 120 angle 2 Convert 315 to radians 4 Estimate and draw a 30 angle 6 Estimate and draw a 90 angle

5 The hypotenuse and one of the legs of a right triangle form an angle that has a cosine of 30 120 90 60 What is the measure of the angle

al information can be used to prove AEFG GE WY

By which rule are these triangles congruent A AAS F J

3 Looking ahead Special right triangles are key to understanding the Unit Circle If the triangle the Unit Circle identify the value of x and y to determine the length of the legs Y

AG is tangent to circle at point A If m AI 108 find m IAG V I A G

ned by points A B C a right triangle L H

32 A group of coworkers decided to buy their boss a 400 birthday gift and to split the cost equally among themselves When three of the coworkers decided not to contribute those remaining still divided the 400 birthday gift equally but each coworker s share of the cost increased by 30 How many coworkers were in the group originally

NOTES Use the figure to find the exact value of each trigonometric function a sin ASK YOUR TEACHER 2 2 b c 7 V 8 100 d cot f csc h X X 9 2 sin cos PRACTICE ANOTHER ir 0 0 8 6

5 Determine the number of degrees in the unknown angle labeled Then convert all ang Degrees 43 108 47 103 TROVIZOJ Radians 7 43 108 103 47 grees Which angle is greater in

1 The number of radians in a 275 angle can be expressed as k where k is a constant What is the value of k a b c 312 55 36 36

G 5 Find the measure of each of the numbered angles Explain your reasoning for each angle A D 10 3x 25 63 6 From the diagram find B 5 2 C 2x LL 65 a the length of BC b mZA c the value of x Give reasons for your answers E 3 110 5x D

What is the length of line segment UF AFGH AFUV 132 D D A B 55 48 121 60 65 87 H

The triangles in each pair are similar Find the length of segment SQ Q X R 3 S 15 12 Y 9 N

Find the length of AB A B 7 in Round to the nearest whole number nearest wh he length of arc AB is approximately

Given right triangle DEF what is the value of cos F F D 9 A B C 41 40 41 40 40 41 E

C D 3 C B 6 B Carl is attempting to find the value of x 6 12 He set up the proportion 9 12 x If Carl is correct what should his answer be If Carl is incorrect what is the correct proportion and answer A 12 E X Carl is correct and x 24 Carl is correct and x 6 6 Carl is incorrect because the proportion should be 12 3 x and x 1 5 Carl is incorrect because he cannot find x due to lines BE and CD not being parallel

13 W 16 19 C 22 X A D B C D B 14 17 B E D B A E 20 B 23 D B 15 A D C C B 18 X W 21 R B D 24 M E A 9

Items 3 and 4 refer to the figures below A 5 B 8 AABC AZYX a C x X 27 24 Y X Z 3 Find the measure of sides a and x 4 Name the pairs of angles that are congruent

1 A 30 foot long support wire for a 16 foot high streetlight runs from the top corner of a building to a point on the ground forming a straight line The length of the wire from the top of the building to the top of the street light is 6 feet How tall is the building

A writer s salary was 81 34 per assignment After a promotion and a raise her salary is now 88 51 per assignment To the nearest tenth of a percent by wha percent did the writer s salary increase A 7 2 B 8 1 C 8 8 D 9 3

h x Some values of the linear function h are shown in the table above What is the value of h 6 A 14 B 15 C 16 D 17 1 3 3 5 7 21

Number of U S Presidents Aged 60 or Younger when Inaugurated 56 57 58 60 55 54 52 50 51 49 Age 42 47 48 43 46 4 1 1 Frequency 1 3 1 2 15254 2 1 2 here are 35 U S Presidents who were 60 years old or unger when they were inaugurated as shown in the e above Based on the table what was the median For these 35 presidents 1

Use the information and diagram below to answer questions 4 5 In the diagram above of ACDE where FD is an altitude drawn to hypotenuse CE 4 If CE 20 and CF 4 what is the length of DF in simplest radical form A 8 B 4 5 C 12 D 16 5 5 What is the area of ACDE in simplest radical form A 80 B 48 5 C 160 D 96 5 C F

Solve the right triangle Z 510 10 Y

Solve the right triangle W 5 9

6 Find XZ 9 X 50 Z

SSA Determine if the two triangles are congruent If they are state how you know Not enough information AAS HL

7 Which of the following could be used to solve for mLA Select all that apply a mA sin b mA tan c mA cos d mzA tan 1 1 24 25 A 25 24

nd the six trigonometric functions of the given angle by hand 77 6

Choose ALL answers that describe the quadrilateral OPQR if m 0 101 m P 68 m Q 146 and m R 45