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kari74 [83]
3 years ago
10

Find 2004-04-02-04-00_files/i0340000.jpg. Round the answer to the nearest tenth.

Mathematics
1 answer:
lesya692 [45]3 years ago
7 0

<span>The problem is to calculate the angles of the triangle. However, it is not clear which angle you have to calculate, so we are going to calculate all of them
</span>
we know that
Applying the law of cosines
c²=a²+b²-2*a*b*cos C------> cos C=[a²+b²-c²]/[2*a*b]
a=12.5
b=15
c=11
so
 cos C=[a²+b²-c²]/[2*a*b]--->  cos C=[12.5²+15²-11²]/[2*12.5*15]
cos C=0.694------------> C=arc cos (0.694)-----> C=46.05°-----> C=46.1°

applying the law of sines calculate angle B
15 sin B=11/sin 46.1-----> 15*sin 46.1=11*sin B----> sin B=15*sin 46.1/11
 sin B=15*sin 46.1/11-----> sin B=0.9826----> B=arc sin (0.9826)
B=79.3°

calculate angle A
A+B+C=180------> A=180-B-C-----> A=180-79.3-46.1----> A=54.6°

the angles of the triangle are
A=54.6°
B=79.3°
C=46.1°
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<span>I chose a box of cereal-------> rectangular prism
</span>see the attached figure

Part 1)<span>List the dimensions of your box. Be sure to include the units (in, cm, ft, etc.).
Length: 20 cm
Width: 8 cm
Height: 32 cm

Part </span><span>2).
 Describe the shape of the cross-section when the box is cut parallel to the base

the shape of the </span>cross-section <span>would be a rectangle of dimensions
20 cm x 8 cm

Part 3)
</span><span>What is the surface area of the box? 
</span>
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perimeter of the base=2*[20+8]-----> 56 cm
height=32 cm

surface area=2*160+56*32------> 2,112 cm²

the answer part 3) is
2,112 cm²

Part 4)
<span>What is the surface area of the box if it is scaled up by a factor of 10?
</span>
we know that
surface area of the larger box=[scale factor]²*surface area original box

scale factor=10
surface area original box=2,112 cm²
so
surface area of the larger box=10²*2,112-----> 211,200 cm²

the answer part 4) is
211,200 cm²

Part 5) 
<span>What is the volume of the box?
</span>
volume of the box=L*W*H-----> 20*8*32------> 5,120 cm³

the answer Part 5) is
5,120 cm³

Part 6) 
<span>What is the volume of the box if it is scaled down by a factor of 1/10

we know that
volume of the smaller box=[scale factor]</span>³*volume original box
scale factor=1/10
volume original box=5,120 cm³
so
volume of the smaller box=[1/10]³*5,120-----> 5.12 cm³

the answer part 6) is
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