Solution of triangles Questions and Answers

What is an angle An angle is I

6 5 4 3 2 S N 65 3 2 1 51 67 hut 1 2 3 42 Write an equation for the graph above f x est 16

Use the Law of Sines to solve if possible the triangle If two solutions exist find both Round your answers to two decimal places If a triangle is not possible enter IMPOSSIBLE in each corresponding answer blank A 139 a b 16 B C C

12 1 point D C 50 degrees 90 degrees Previous A If the measure of arc AB is 50 degrees what is the measure of angle ADB 25 degrees 100 degrees B

0 6 25 Points Determine two coterminal angles one positive and one negative for each angle Give your answers 19t 8 a DE b 8 0 rad 7T 15 rad

Find the indicated side x if b 6 a 33 y 70 Use either the Law of Sines or the Law of Cosines as appropriate 3 354 22 369 5 164 a X B

The point is on the terminal side of an angle in standard position Find the exact values of the six trigonometric functions of the angle 9 4 sin 0 cos tan 8 CSC 0 sec 0 cot 0

Find all angles between 0 and 180 satisfying the given equation Round your answer to one decimal place Enter your answers as a comma separated list tan 0 7 0

Find the measure of angle A 9 Fa 71x 1 11 0 x 51 20x x 61 80 A 28 28 10 A 12 x 34 otsib olgua does lo ozess x 64 x 52 75 67 x

Find a cofunction with the same value as the given expression csc 5 Select the correct choice below and fill in the answer box to complete your choice Simplify your answer Type any angle measures in degrees Do not include the degree symbol in your answer A csc 5 tan csc 5 sec 85 Oc csc 5 cot OD csc 5 sin

20 A ray that divides the angle into two angles is the angle bisector 21 An obtuse triangle has exactly one angle whose measure is greater than 90 biosoqsil 22 Suppose a set of thin rods is glued together into a triangle as shown How would you place the triangular arrangement of rods onto the edge of a ruler so that they balance Explain why

Use the Pythagorean Theorem to find the missing length in the right triangle Use a calculator to find square roots rounding to the OA 22 5 km OB 4 5 km OC 6 7 km OD 45 0 km

3 Scientists measure the depths of lunar craters by measuring the length of the shadow cast by the edge of the crater using photos In a photograph the length of the shadow cast by the edge of the Moltke crater is about 606 metres given to the nearest metre The sun s angle of elevation is 65 Find the depth of the crater giving your answer rounded to the nearest metre

A triangle has a base length of 3 1 cm and corresponding height 4 2 cm correct to 1 decimal place Calculate the upper and lower bounds for the area of the triangle as accurately as possible 4 2 cm 3 1 cm

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

Given A ABC find the value of the variable If necessary round your answer to the nearest hundredth Figure is not to scale A 77 27

1 Given f x 2x and g x x 4 determine the expression for f g x

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

To get a good view of a person in front of a teller s window it is determined that a surveillance camera at a bank should be directed at a point 22 4 ft to the right and 10 4 ft below the camera as shown in the figure to the right At what angle of depression should the camera be directed What is the angle of depression A 0 tonth as pooded Y 22 4 ft 10 4