Solution of triangles Questions and Answers

Complete the following sin 116 81 ing O cos A sin

6 Determine the length of side x to the nearest inch X 16 12

Express cos U as a fraction in simplest terms U 30 94 T S

help Given right triangle ABC with altitude BD drawn to hypotenuse AC If AD 3 and DC 11 what is the length of BD in simplest radical form A B 3 Answer BD D 11 Submit Answer 30

Express tan B as a fraction in simplest terms 28 B D 55 C

The triangle below is equilateral Find the length of side a in simplest radical form with a rational denominator 10 X

3 In a circle with center O central angle AOB has a measure of radians The area of the sector formed by central angle AOB is what fraction of the area of the circle 2 points a b C d 74 780 IN H 7 O A OB O C

JL and NL are secants to Circle O What is the value of angle L 125 N 92 Type your answer D K B 51 1 point What is the measure of E E M L 140 C

3 1 point What is the measure of x 16 14 2x 5 6 x 11 Type your answer 1 point What is the measure of x 15 Tyne your answer

Q3 Calculate the side or angle marked with a letter 11 51 2 9 31 Q4 B D D A 90 C D 32 4 B A 41 and AD 100 cm Calculate a the length of AB b the length of DC c the length of BD B A 32 4 100 cm 41 L

21 L 18 14 X 20 Q 12 R The polygons are similar Find the value of x

x E X 20 D 16 F 15 H 18 G 12 J The polygons are similar Find the value of x

2 Solve for b in the triangle to the nearest hundredths A C 8m 25 B

Review Key Concepts The measure of an inscribed angle is half the measure of its intercepted arc Two inscribed angles that interceptthe are congruent An angle inscribed in a semicircle is a angle The opposite sides of a quadrilateral inscribed in acirde are supplementary If a tangent and chord intersect on a cirde the measure of each angle they form is the measure of its intercepted arc

The First Corollary to the Inscribed Angle Theorem First corollary to the inscribed angle theorem Two inscribed angles that intercept the same arc are congruent ZKJL and ZKML are their angles intercept the same arc KL same A JM because We can also say that JKM and congruent because their angles also intersect the are J K M

Angle BAC measures 56 D B O What is the measure of angle BDC O 28 O 34 O 56 O 112

Justifying the Second Corollary to the Inscribed Angle Theore Explain how you can use the inscribed angle theorem to justify its second corollary that an angle inscribed in a semicircle is a right angle

For triangle ABC we are given that mZC 89 1 AC 12 3 ft and BC 23 3 ft We can use the Law of Cosines Law of Sines and other properties of triangles to determine all of the missing information Note that the diagram may not be drawn to scale a AB B Determine all of the missing information about this triangle d m B 23 3 ft feet Preview b Draw the triangle and add the length of AB to your diagram c m A degrees Preview degrees Preview 89 10 A 12 3 ft

QR is tangent to circle P at point Q Q R 5 3 3 P What is the approximate length of RP Round to th nearest tenth O 5 6 units 6 1 units 8 3 units O 9 8 units

An automated machine is calibrated to fill bags of pretzels so that each bag weighs 8 ounces A worker at the factory believes the machine is not filling the bags to the correct weight She randomly selects 40 bags of pretzels and after weighing them calculates their mean weight to be 8 4 ounces Write null and alternative hypothesis to describe this situation 1 point O H p 8 H p 8 OH 8 H 8 OH 8 4 H 8 4 H 8 H H 8

Problem 6 Solve for the missing sides and angles b 3m

1 What is the m C B A 25

The table below gives the typical number of days of rainfall in Fall and Spring in Death Valley California Fall Event F Spring Event S Rain Event R 7 No Rain or Dry Event D 115 Given the fact that it rained one day in the Fall or the Spring how much more likely is it that the day it rained was in the Fall o 1 13 122 244 01 6 116 265

E3o luo ulo 1 Solve 1 of the 2 problem below Solve the triangle s find all sides and angles a 4 b 5 c 6 ers Angle A 40 Angle B 60 B 5 wood 21 lo sigas ne tihw Jisus 30 501 516 57q8 ml woll 2791 8 1001 201 to slam mais

6 Solve Pick 2 of 5 equations to solve algebraically Find the general formula AND all the solutions in the interval 0 2n or 0 360 00 9m6 2 MAX3 3165979 2sin x 2 1 2cos x cosx 0 3sin2x sinx 4 0 2cos 2x 2 tan x 1 2 Juo tiqa bns Juo tiqa bos 2 169 fregrist bris gniz00912 I 169 Inggrist 9219vni 9200 9219vni9niz 9thW deixe Jon 290b ji ti benitsbnu 9 tal 6920 ton od gulsv to6x9 90 bmi S 9u b9b99n 26 9it wod 10 glorio finu to rotexe riguon Vrniz niz niz T niz niz

A 85 b 127 c 266 B C a 266 m G 859 127 m Carry your intermediate computations to at least four decimal places Round your answer to the nearest tenth of a meter

The Venn Diagram below models probabilities of three events A B and C A blue green B green yellow C Red only The probabilities for each event are given by the ratio of the area of the event to the total area of 72 For example E C is Red Only Area of Red Total Area So for the probability of Event C you have P C 18 1 18 12 6 72 4 0 25

chosen at random find each probability 13 P has at least 4 sides not a hexagon 15 P not an octagon I not a triangle ugons and the rest are octogons It a fie is 14 P not a square has less than 7 sides 16 P octagon sum of interior angle measures is at least 600

1 P even at least 12 at random Find each probability 2 P perfect square odd

What is the value of 0 in the diagram below A B C D 32 2 40 2 49 8 57 8 13 11 8

A magazine contains fourteen pages You open to a random page What is the probability that the page number is three or seven

Find the exact value of tan Q in simplest radical form 38 6 S 2 R

Find the exact value of tan J in simplest radical form J 4 I 7 33 H

Evaluate cos sin H Select Select 77 7 b Select

Find the exact value of cos F in simplest radical form 95 D 5 70 E

Find the exact value of tan G in simplest radical form 74 E G 4 58 F

5 Calculate the area of the shaded region when the square is inside of the rectangle below 8 2

Find the exact value of sin J in simplest radical form L V99 18 K J 15

Show Transcribed Text b c 24 Which of the following are x intercepts of the function 00 12 Dao d SE e F f 68 VV 5

y tan TC y tan x x 3 CLEE NO y tan x Drag each of the functions given above into the appropriate area below depending on which function is represented by which graph 1 2 Q KN y tanx O O

13 What is the perimeter of AXYZ Y 7 5 X B 6

Let the expression m A n be defined to mean 2mn m Then 3 5 A 7 X x X X X A 225 B 105 C 75 D 210 X E 1 of 10 06 16 II 280

Solve the triangle A 37 C 95 c 18 for b

88 8 cos M cos N sin M sin N 32 P 1111 1 1 1 1 1

etric equations x x x x t y y y y t where 0 St 1 describe the line segment that joins the points P x y and P x Y Use a graphing calculator or computer to draw the triangle with vertices A 1 1 B 5 4 C 1 6 Find the parametrization including endpoints and sketch to check Enter your answers as a comma separated list of equations Let x and y be in terms of t from 0 1 4t 1 3t AB BC AC X ASK YOUR

A ship leaves Port A and travels 73 km due west to Buoy C It then adjusts its course 66 northward It travels 123 km in that direction until it reaches Port B What angle with respect to due west could the ship have used to travel directly from Port A to Port 82 See the figure below The figure is not drawn to scale Port B 123 km 66 Buoy C 23 km Port A Carry your intermediate computations to at least four decimal places Round your answer to the nearest tenth of a degres

You are on a fishing boat that leaves its pier and heads east After traveling for 25 miles there is a report warning of rough seas directly south The captain turns the boat and follows a bearing of S35 W for 14 2 miles a At this time how far are you from the boat s pier b What bearing could the boat have onginally taken to arrive at this spot 142 MA

The vertices of AABC represent the buoy markers that form the legs of the course for a swim race What is the distance from marker C to marker A Round your answer to the nearest tenth of a meter 60 O 130 5 m O 148 4 m O 175 9 m O 269 5 m 200 m 40 B

You hike 210 meters up a steep hill that has a 31 angle of elevation as shown in the diagram A 210 m 31 b B a C Give each side and angle measure rounded to the nearest whole number a mZB III

35 cos M cos N sin M 37 sin N N 12 HIII 1 T 1 1 1 T