Part 1) we know that m∠5=44° m∠11=86° m∠2=m∠5------> by vertical angles m∠2=44° m∠13=m∠11------> by vertical angles m∠13=86° m∠12+m∠13=180°-----> supplementary angles m∠12=180-86-----> m∠12=94° m∠14=m∠12----> by vertical angles m∠14=94° m∠1=m∠11----> by corresponding angles m∠1=86° m∠4=m∠1----> by vertical angles m∠4=86° m∠2+m∠1+m∠6=180 m∠6=180-(86+44)----> 50° m∠6=50° m∠3=m∠6----> by vertical angles m∠3=50° m∠8=m∠3----> by corresponding angles m∠8=50° m∠8+m∠7=180°-----> supplementary angles m∠7=180-50----> 130° m∠7=130° m∠10=m∠6----> by corresponding angles m∠10=50° m∠10+m∠9=180°-----> supplementary angles m∠9=180-50-----> 130° m∠9=130°
the answers Part 1) are m∠1=86° m∠2=44° m∠3=50° m∠4=86° m∠5=44° m∠6=50° m∠7=130° m∠8=50° m∠9=130° m∠10=50° m∠11=86° m∠12=94° m∠13=86° m∠14=94°
Part 2) a) what is m∠TPR? in the right triangle PTR m∠PTR+m∠TPR+m∠TRP=180° ( the sum of internal angles of triangle is equal to 180 degrees) m∠PTR=30° m∠TRP=90° so m∠TPR=180-(90+30)----> 60°
the answer Part 2a) is m∠TPR=60°
b) what is the length in inches of segment PR? in the right triangle PTR sin 30=PR/TP-----> PR=TP*sin 30-----> PR=14*(1/2)----> 7 in
the answer Part 2b) is PR=7 in
c) what is the length in inches of segment TR? in the right triangle PTR cos 30=TR/PT-----> TR=PT*cos 30-----> TR=14*(√3/2)---> TR=7√3 in
the answer Part 2c) is TR=7√3 in
d) what is the length in inches of segment PQ? in the right triangle PQR PR=7 in RQ=PR-----> by angle 45° so RQ=7 in applying the Pythagoras Theorem PQ²=RQ²+PR²-----> 7²+7²-----> PQ²=98-----> PQ=√98 in---> PQ=7√2 in
the answer Part 2d) is PQ=7√2 in
Part 3) Patrice buys a block of wax in the shape of a right rectangular prism. The dimensions of the block are 20 cm by 9 cm by 8 cm. <span><span>(a) </span>What is the volume of the block?
volume of the prism=20*9*8-----> 1440 cm³
the answer Part 3 a) is the volume of the block is 1440 cm³ <span> Patrice melts the wax and creates a candle in the shape of a circular cylinder that has a diameter of 10 cm and a height of 15 cm.<span>(b) </span>To the nearest centimeter, what is the volume of the candle? </span></span>volume of a cylinder=pi*r²*h diameter=10 cm radius r=10/2----> 5 cm h=15 cm volume of a cylinder=pi*5²*15----> 1177.5 cm³-----> 1178 cm³
the answer Part 3b) is the volume of the candle is 1178 cm³
<span>Patrice decides to use the remaining wax to create a candle in the shape of a cube.<span>(c) </span>To the nearest centimeter, what is the length of the side of the cube? </span> the remaining wax=volume of the prism-volume of a cylinder =1440-1178-----> 262 cm³
volume of a cube=b³ where b is the length side of the cube 262=b³-------b=∛262-----> b=6.40 cm-----> b=6 cm
the answer Part 3c) is the length of the side of the cube is 6 cm
