Circles and Triangles

Week4:Assignment4

Pleaseanswerthefollowingquestions.Someofthequestionsarefromyourtext.

1.       Anairplanereachesanaltitudeof3miabovetheearth.Assumingacleardayandthatapassengerhasbinoculars,howfarcanthatpassengersee?(Hint:Theradius oftheearthisapproximately4000miles[CD1] )

2.       Statethemeasureoftheangleformedbytheminutehandandthehourhandofaclockwhenthetimeisa)1:30pmandb)2:20am[CD2] . 

(Clock 1:30)                                        (Clock 2:20)

Clock: each 5 minutes equals 30° in the circle (360/12=30). Each minute equals 6°  (30/5=6) 

For the 1:30 clock -  four arcs of 5 minutes equals (4*30=120) 120°. The 1 represents half of an arc  or two and half minutes (6*2.5=15) 15°  120+15=135°  The angle when the clock is at 1:30 measures approximately 135°.

The 2:20 Clock: The 3 to 4 arc equals 30°. The second arc covers 3.5 minutes (look at the hour hand) 6*3.5= 21° the angle when the clock is at 2:20 measures approximately 51°.

3.       SupposethatacircleisdividedintothreecongruentarcsbypointsA,B,andC.Whatisthemeasureofeacharc?WhattypeoffigureresultswhenA,B,andCare joinedbysegments[CD3] ?

Answer: Congruent arcs are arch in the same circle or in congruent circles that measures the same in degrees (Week Four: Arcs and Central Angles). A circle measures 360°. 360/3 (three congruent arcs) = 120° each. The figure form by segments ABC is a triangle.

****I tried to make to a circle to show the shape****

                                                                        A

        C

                                                                            B

4.       Answerthefollowingproblemfromyourtextbook:Problem29,Section6.2.

For the five pointed star (pentagram), inscribed in the circles, find the measures of angle 1 and 2[CD4] .

(Alexander 298)

Polygon Sides =(number of sides -2)*180°  

(Alexander 102)

The inside polygon = (number of side -2)*180 = (5-2)*180

The polygon total angles =540°  each angle inside the polygon = (540/5)=108°

∠2 = 108°

To calculate ∠1, I need to  subtract 180°-108° =72°     72+72+x=180

144+x=180

X=180-144

X=36

∠1=36°

     ∠1       

                                    ∠2 = 108°

The measurement of the angles are 36° and 108°.

5.       Thelengthsofthelegsofarighttriangleareconsecutiveevenintegers.The numericalvalueoftheareaisthreetimesthatofthelongerleg.Findthelengthsofthelegsofthetriangle.

(Hypotenuse)² = (leg 1)² + (leg 2)² (Week 3:Pythagorean Theorem[CD5] ).

   =x

=X+2

(Alexander 140)

Area of a triangle = a =1/2bh

A = numericalvalueoftheareaisthreetimesthatofthelongerleg

3(x+2)= x*(x+2)

                          2

3x+6=x²+2x

             2

6x+12=x²+2x

x²-4x-12=0  This is a quadratic equation

Ax²+Bx+C=0

x²-4x-12=0 (factor )

(x-6)                    (x+2)

x-6=0                  x+2=0

x=6                     x=-2

Checking 6 and -2

Area of the triangle 3(x+2)= x*(x+2)

                                                               2

3(6+2)= 6*(6+2)             3(-2+2)= 6(+2-2)

                       2                                           2

18+6= 48                        0=0      

                       2

24=24        (6ü, -2 does not work)

The numericalvalueoftheareaisthreetimesthatofthelongerleg.

3x=24

X=8

Find the lengths of the legs of the triangle.  The lengths of the legs are 6 and 8.

6.       Answerthefollowingproblemfromyourtextbook:Problem18,Section6.1.

Problem: AB is the common chord of circle O and circle Q. If AB =  12 and each circle has a radius of length 10, how long is segment OQ[CD6] ? 

7.       Answerthefollowingquestionsfromyourtextbook:Problem39,Section6.1.

If arc ST≅ arc TV, explain why ΔSTY is an isosceles triangle[CD7] .

 An isosceles triangle is a triangle that has two congruent sides.

8.       TheradiusofaFerriswheel’scircularpathis40ft.Ifa“ride”of12revolutionsismadein3minutes,atwhatrateinfeetpersecondisthepassengerinacartmovingduringtheride[CD8] ?

The circumference of a circle is calculated by 2(Pi)(r) (Alexander 380). 

2(Pi) (40)= feet per revolution

2(3.141592654)(40) = feet per revolution = 251.3 feet per revolution

12 revolutions per three minutes = 4 revolutions per minute 12/3 = 4

251.3 * 4 revolutions per minutes = 1,005.2  feet per minute

1005.2/60 (seconds) = 16.75 feet per second.

The passengers in a cart of a Ferris wheel will move 16.75 feet per second.

9.       In a given a triangle ABC, AB = 10, BC = 17, and AC = 21cm. What is the area of the triangle[CD9] ?

Work Cited

"Clock 1:30." Educational Technology Clearinghouse. N.p., n.d. Web. 04 July 2014.

"Clock 2:20." Educational Technology Clearinghouse. N.p., n.d. Web. 04 July 2014.

“Week Four: Arcs and Central Angles.” College Math II. The Art Institute of Pittsburgh Online Division, 2014. Web. 4 July 2014.

Alexander, Daniel C., Geralyn Koeberlein. Elementary Geometry for College Students, 5th Edition. Cengage Learning, 01/2010. VitalBook file.