Solution of triangles Questions and Answers

The dimensions of A QRS shown below are in units ata od S Which ratio represents the value of sin Q A B 30 10 2 1 C D co cr 15 9 12 SOR

27 What is cos 314 40 equivalent to OA cos 44 40 OB O C O D cos 44 40 cos 45 20 cos 45 20

K The function graphed to the y a sec bx c or y a cso Determine the equation of t An equation of the function

1 Arrange the following s A B C 1 sin c cos x sin c 1 sin 2 sin sin a sin c sin c sin x 1005 sin

6 Find the exact value of cos 0 given that the tan and angle 8 is in 2 points quadrant II

OA 6249 OB 1 600 O C 1 600 D 6249

In the xy plane the line determined by the points c 3 and 27 c intersects the origin Which of the following could be the value of c A 0 B 3 C 6 D 9

The midpoints of the legs of a right triangle are 3 1 and 1 3 Name the coordinates of the vertices of the right triangle

Solve for x Round to the nearest WHOLE NUMBER X 13 12 K X L S 15 M

Find the value of x Round to the nearest WHOLE NUMBER B 5 X 10 X Z N FILE LE SELLE

1 point A man who is 6 feet tall casts a shadow that is 8 22 feet long How tall is the tree

1 2 1 point What is the approximate value of x rounded to the nearest tenth Type your answer 6 1 point Look at the following triangles below Which postulate could prove they are similar if they similar AA 10 16 5 18 4 14 8

B If ABCD AGEF find the value of x B C 1 point 2x 7 D x type your answer E 51 57 G Natasha places a mirror on the ground 24 ft from the base of a tree She walks backward until she can see the top of the tree middle of the mirror At that point Natasha s eyes are 5 5 ft at the ground and her feet are 4 ft from the image in the mirror the height of the oak tree

For what value of x is A ABC A DEF C 30 B 72 36 A F D 15 72 E 4

1 point 5 M A E D B CAB DE 6 17 5 A B 25 20 E 40 32 D 28 F

Given AJKL ANMP find the value of x K P x 5 17 14 M 49 L 9x 1 X type your answer D 1 point If ADGH ADEF find the value of x 91 52 G E N x 3 2x 1 F

Classic Probability An opaque bag contains 5 green marbles 3 blue marbles and 2 red marbles What is the probability of randomly picking out a marble and the marble being blue 1 2 O 113 115 8

Classic Probability What is the probability of spinning the spinner and the arrow landing on a number that has a spelling that starts with a vowel e g eight starts with a vowel O 1 2 01 O 4 5 6 2 7 1 8

1 3 45 y 10 2 45 X y X 7 Show ALL of your work for full credit 2 b 4 9 2 45 a b 14 45 a

The terminal side of an angle in standard position measuring 6 intersects the unit circle at b c In terms of b and c what ordered pair represents the coordinates of the point where the terminal side of the angle measuring 354 intersects the unit circle Provide your answer below

the diagram shows a boat that is anchored at point 8 in a river There are two boat ramps on the far side of the river shown by points A and C The boat is 120 meters from ramp A and 150 meters from ramp C 120 m 110 1 m ABC 110 what is the approximate distance between the two boat ramps to the nearest meter Enter the answer in the box 150 m

Triangle JKL is similar to triangle PQR Solve for t J 4 5 5 1 5 K t R 25

The angle 810 rotates full time s around the origin and is radians

The Peachtree Plaza hotel in Atlanta Ga is approximately a cylinder A building inspector is attempting to approximate the interior volume of the building to determine if the building has proper heating and cooling Determine the volume of the building given that it has a height of 723 feet and a diameter of 187 feet 6 618 966 cubic feet 19 856 897 cubic feet 26 475 863 cubic feet 79 427 590 cubic feet 187 ft E 723 ft

Q4 In the diagram A B C are points on the circumference of a circle and the line AB is the diameter A 46 B b Find the size of angle x giving reasons for your answer b Find the size of angle y giving reasons for your answer 2 2

A02 Q7 B is a point on the circumference of the circle O is the centre of the circle and the line AB is a tangent to the circle a Find the size of angle x b Find the size of angle y 0 B 64 x B Q8 A02 A B C and D are points on the circumference of a circle and O is the centre of the circle The line EF is a tangent to the circle E 1 1

segment ab is on the line y 3 2 x 2 and segment cd is on the line y 3 1 2 x 2 which statement proves the relationship of segments ab and cd a they are Parallel because they have the same slope of 2 b they are parallel because they have the same slope of 1 2 c they are perpendicular because they have slopes that are opposite reciprocals of 2 and 1 2 d they are perpendicular because they have slopes that are opposite reciprocals of 2 and 1 2

a Find an equation of the tangent line at x a b Use a graphing utility to graph the curve and the tangent line on the same set of axes y e a In 10 a At x a an equation of the tangent line is y

27 Question 27 30 A 2x Multiply simplify completely 2x 1 x 4x 5 9x 6x 5 7x 14x 5 2x 7x 6x 5 9x 14x 5 B 2x3 2 2 0

What are the solutions to the equation z 9 0

Given AABC ADBE Which proportion must be true O A BC BE AD AC EC CA BE AC 211 211 AC DE DC CA BC CA EC BD B E C

1 point Why are these triangles similar 1 A O O O O SAS SSS AA Triangles are not similar 4 1 point Why are these triangles similar 9 SSS 6 SAS 2 Triangles are not similar 3

5 Why are these triangles similar B Q 9 M OO Triangles are not similar SSS 1 point What is the similarity ratio of these triangles P 12 X AA SAS A X 9 15 3 4 1 2 15 20 16 L 12 W

LO 1 point Why are these triangles similar 6 10 12 10 SAS AA SSS Triangles are not similar 1 point What is the similarity ratio of these triangles 6 12 00 10 8 1 2 4 5 5 5

Directions Complete the following tables Show all work on a separate sheet of paper If the angle measure is greater than 360 or 2n find the positive coterminal angle between 0 and 360 first Radian Measure Degree Measure Sin Cos Tan Cot Sec Csc Radian Measure Degree Measure Sin Cos Tan Cot Sec CSC 8T 3 3 2 330 540 3x 4 7 3 450 150 H 6 13t 4 135 5m 210 240 7 T 4 270

24 An equation is shown x 2x 10 B Which expression is a solution to this equation A 1 3i 8 1 6i c 1 3i D 1 6i

Factor the polynomial if possible If the polynomial cannot be factored write prime z 32 12 12

1 ADEF where ZD is a right angle and DE DF If EF 10 what is the length of DE in simplest radical form Draw and label a triangle first

1 In right triangle XWY shown in the diagram above altitude VW is drawn to hypotenuse XY WY 13 and VY 12 a Determine the length of VW b Determine the area of AVWY c Set up an equation to find the length of VX d Solve for the length of VX W Y

Let AABC be a triangle and let the interior angle bisector at A intersect the side BC in point D Show that B A D BD IDCI C TABL IACI Hint Construct the line through B parallel to AD and extend AC to let it intersect this line in E Show that JARI LATI

Using the diagram attached assume angle DAB angle CAE and AD AE Prove that triangle ABC is isosceles To do this please only use ideas from Euclid s Propositions 1 1 1 26 nothing after that

Based on the measures provided in the diagram determine the measure of MNH You may assume that point C is the center of the circle and that MH and GN are diameters Figure may not be drawn to scale 255 75 105 180 H G 105 O N M

6 cm 3 In right triangle ABC shown in the diagram above altitude AD is drawn to hypotenuse AC DB and DC 10 cm A a Find the length of AB in simplest radical form Heartbeat or Boomerang Proportion b Find the length of AD in simplest radical form Heartbeat or Boomerang Proportion B D V

er the following question 2 Match the correct answers rhombus MNOP N Complete this informal proof You are given that MNOP is a rhombus Prove that MO bisects NMP and NOP and that NP bisects MNO and MPO MNOP is a rhombus Given MN MP NO PO Def of SAS MO XCPCTC M AMNO AMPO parallelogram 21 22 23 24 CPCTC NP NP MO bisects LNMP and ZNOP Def of XCPCTC NO NM PO PM Def of XNP Reflexive Prop of APMNA parallelogram 252 26 47 48 bisect P Reflexive Prop of NP bisects MNO and MPO Def of SSS XCPCTC

1 Match the correct answers Given MNOP is a kite Prove NP P Statements 1 MNOP is a kite 2 MN MP NO PO 2 Def of a 3 MO MO 5 ZN P a SSS b CPCTC C SAS d Reflexive Property of Reasons 1 Given e kite f rhombus g AMNO AMPO h Symmetric Property of 5

Find the missing length indicated 65 25 O 121 O 136 X O None of the other answers are correct O144

A triangle has legs which measure 15 inches and 20 inches Find the length of the hypotenuse O 25 inches O 13 inches O 32 inches O 28 inches

Find the missing length in the right triangle 6 ft O None of the other answers are correct O 10 ft 8 ft O 12 ft

amplitude period y 5 sin x horizontal shift Graph one complete period y 4 2 2 4 y period and horizontal shift of the function 1 0 0 5 2 2T X X y 4 2 2 4 y 4 2 5 2T 2 X X

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