Solution of triangles Questions and Answers

Find the cosine of ZJ J 13 5 I 12 K Write your answer as an integer or as a decimal rounded to the nearest h cos J

2 Using the diagram below find the measure of ZC to the nearest degree B A 37 12 6 cm D 22 5 cm C

36 Express 1 2 sin 38 as a function of twice the given angle A cos 76 sin 76 sin 76 OB O C D cos 76

12 To answer questions 12 17 use the formulas for functions of the difference and sum of two angles to find without tables or calculator the cosine sine and tangent of the angle 15 using 45 and 30 sin 15 A sin 45 cos 30 cos 45 sin 30 B cos 45 cos 30 sin 45 sin 30 C cos 45 cos 30 sin 45 sin 30 OD sin 45 cos 30 cos 45 sin 30

19 To answer questions 18 20 use the formulas for functions of the difference and sum of two angles to find without tables or calculator the cosine sine and tangent of 255 cos 255 O A B 6 2 4 OC 2 6 4 O D 6 2 4 6 2 4

10 Simplify A B O C D cos 30 8 cos 30 8 sine 3 sin e sine 3 sine

O4 in O 8 in O 2 in O not enough info 2 Find y 54 1 ABC is an equilateral triangle overline CD is a perpendicular bisector to AB Find the measure of AD 126 O 126 0 not enough

60 06 09 12 60 bx 30 O not enough information 36 4 Find the measure of the vertex angle

The exterior angle sum of every polygon is always 360 True False

The perimeter of AABC 300 centimeters AB 75 BC 125 Which statement is true about the interior angles of AABC O ZA is the largest angle O Bis the largest angle LC is the largest angle ZA is the smallest angle O O

Complete the proof of the identity by choosing the Rule that justifies each step 1 1 cot x To see a detailed description of a Rule select the More Information Button to the right of the Rule 1 cosx 1 cos x Statement 1 cosx 1 cosx 1 cos x sin x 11 1 CSC x 2 Rule Rule Rule Rule Rule

As shown in the diagram below AC bisects BAD and zB D Which method could be used to prove AABC AADC OA SAS OB SSS O C AAA O D AAS

What value of x makes ACATABOY C 4x 5 O A 5 OB 7 C O C 0 5 A 3x 4 2x 3 T 5x 12 6x 5 6x 11 B

1 Find the length of AB Round to the nearest tenth A i CD ii BD iii AB iv AC B Solve for AB to the nearest tenth 9 30 a Which sides will you need to solve for before solving for AB Select all that apply 270

1 In right triangle GEF below EG 5 cm and FG 12 cm Determine the length E G F

2 Using the right triangle determine the value of h 18 100 meters

The cone below has a volume of 4032 cubic units Find the slant height L given the measures shown 8 L 32

6 Write solve an equation to find the value of x then find the measures of all interior AND exterior angles 2x 7 5x 3 4x 11 7 What is the sum of the measures of the interior angles in a regular dodecagon 8 What is the measure of each interior angle 9 What is the measure of each exterior angle 10 What is the sum of the exterior angles

4 Draw a rotation diagram for each of the following radian angles which are expressed in terms of pi Then determine the reference angle for each also in terms of pi Think back to how you did this with degrees a 2 3 b 11 6 c 5T 4

5 50 10 7 C X 4 18 B Find the measurement of the missing side indicated 5 98 3 20 4 98

28 23 0 15 Vo Find the measure of the indicated angle round to the nearest tenth 55 2 9 4 19 4

40 W 28 cm sin 40 28 w tan 40 w 28 What is the correct equation sin 40 w 28 cos 40 v

8 ed out of Given the graph 10 19 TURI 7 19 19 Find the following 7 7 2 1 0

Given f x x 2 and g x 4x Which of the following represents f g x 4x 2 B 4x 8x 8x 4 4x x 2 D 4x 24x 48x 32

2 In right triangle ABD above AB 14 ft Determine the length of CD to the nearest tenth of a A 65 20 D

1 7 36 C Sine X B Choose the correct trig function Tangent Cosi

Determine the value of x shown in the diagram Figure may not be drawn to scale X 19 x 20 x 405 x 450 12 13 25 21 7

10 tan 62 10 x 62 X Which equation would you use to solve for x sin 62 10 x cos 10 x 62 tan 62 x 10

19 22 Tangent A Choose the correct trig function Cosine

1 Each representation below is an exponential function of the form y a b Find the a and b values for each and write the equation Complete the missing values in the table a 0 1 2 3 4 Equation y 2 10 b Equation 0 10 1 5 c Equation X 0 y 1 6 2 3 54

8 Inverse sine 15 X What is the most efficient way to find x Inverse tangent Inverse cosine Pythagorear

ine Choose the correct trig function Tangent Co

D What is JL A 9 B 12 5 17 5 D 25 K 12 L M 16

20 50 Figure 6 Using Figure 6 above what is the mZX 40 S 100 50 T P R y Q

O The always wrong triangle O Left Triangle 8 Right Triangle O Correct Triangle 12 C Figure 1 Using Figure 1 above yes Figure 1 again name the type of triangle pres in the figure 8

A point on the terminal side of angle 0 in standard position is given Find the exact value of csc 0 sec 0 and cot 0 10 24 Select the correct choice below and fill in the answer box to complete your choice OA csc 8 Simplify your answer including any radicals Use integers or fractions for any numbers in the expression OB The value of csc 0 is undefined

1 In right triangle ABC mzA 90 following is true a sin B sin C b sin C cos C c sin B cos C d cos C tan B

A passenger in an airplane flying at an altitude of 13 kilometers sees two towns directly to the left of the plane The angles of depression to the towns are 12 and 22 How far apart are the towns Round to two decimal places as needed Show your work here

The speed of a particle is defined by the function v t t 2 4 Which equation accurately represents the function for time t At 2 3 v 4 B t 2 v 4 Ot 2 v 4 Dt 2 v 4

29 What is the most specific name for quadrilateral WXYZ with vertices W 0 0 X 3 4 Y 6 0 and Z 3 4 O A OB O C O D A parallelogram B rectangle C rhombus D trapezoid 1

8 AEFG with E 1 4 F 1 2 G 3 6 is drawn on heavy cardboard and then cut out Find the coordinates of the point from which the triangle can be balanced What is the name of this point of concurrency

YOU DO ROUND 2 2 An airplane is 2 miles above the ground and the angle of depression from the airplane to a tree is 15 Determine in miles the length from the airplane A to the tree C 2 miles B 15

a Two trigonometric ratios equal to 8 17 b Two trigonometric ratios equal to 15 17 A 15 2 18 1 17 B 8 C

6 In the triangle below the sine of x is 0 6 What is the cosine of y Ma

Sin A a 42 Sim B b 21 b 70 Sn C C A2 42 B C Solve tring ABC were A 42 6 70 b 122 e b C 70 122

4 In a right triangle one angle measures x where sin x 5 What is cos 90 x

7 In scalene triangle ABC shown in the diagram below mzC 90 Which equation is always true a sin Asin B 3 14 S b cos A cos B DRA C cos A sin C d sin A cos B A C B as Kec les

Based on the diagram and congruent marks what would be a correct congruence statement and the most likely reason the triangles might be congruent K E O A AJKE ALYE because ASA O B AJKE ALYE because AAS O C AJKE ALYE because SAS O D AJKE ALYE because of SSS L

M 1 Given LN NP and MN NO O N 2 IF HG and FG IH F G List 3 parts ALNMA List 3 parts by

In AVWX x 680 inches m X 15 and m V 116 Find the length of w to the nearest 10th of an inch