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2 years ago

Use the law of sines to find the length of side c

Mathematics

1 answer:

AnnyKZ [126]2 years ago

8 0

Answer:

B. 44.93

Step-by-step explanation:

The law of sines states
$\frac{a}{sinA} = \frac{b}{sinB} = \frac{c}{sinC}$

where a, b and c are the 3 sides of the triangle and A is the angle opposite side a, B the angle opposite side b and C the angle opposite side c

In this particular problem we have

side a = 44, angle A = 46.7
side c = ? , angle C = 48

So 44/sin(46.7) = c/sin(48) or by multiplying both sides by sin(48)

c = sin(48) * 44/sin(46.7) = 44.92937 which is 44.93 rounded to 2 decimal places

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allsm [11]

Put them in order from smallest to largest
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answer
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4 years ago

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A glass paperweight has a composite shape: a square pyramid fitting exacty on top of an 8 centimeter cube. The pyramid has a hei

ArbitrLikvidat [17]

Answer:

Part 1) The volume of the paperweight is $576\ cm^{3}$

Part 2) The total surface area of the paperweight is $400\ cm^{2}$

Step-by-step explanation:

Part 1) what is the volume of the paperweight?

we know that

The volume of the paperweight is equal to the volume of the square pyramid plus the volume of the cube

step 1

Find the volume of the pyramid

The volume of the pyramid is equal to

$V=\frac{1}{3}BH$

where

B is the area of the square base

H is the height of the pyramid

$B=8^{2}=64\ cm^{2}$

$H=3\ cm$

substitute

$V=\frac{1}{3}(64)(3)=64\ cm^{3}$

step 2

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The volume of the cube is equal to

$V=b^{3}$

$V=8^{3}=512\ cm^{3}$

step 3

Find the volume of the paperweight

$64\ cm^{3}+512\ cm^{3}=576\ cm^{3}$

Part 2) what is the total surface area of the paperweight?

we know that

The total surface area of the paperweight is equal to the surface area of 5 faces of the cube plus the lateral area of the pyramid

step 1

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$SA=5b^{2}$

$SA=5(8^{2})=320\ cm^{2}$

step 2

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$LA=4[\frac{1}{2}bh]$

$LA=4[\frac{1}{2}(8)(5)]=80\ cm^{2}$

step 3

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$320\ cm^{2}+80\ cm^{2}=400\ cm^{2}$

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alekssr [168]

Answer:

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Step-by-step explanation:

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3 years ago

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Answer:

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Part A:

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Answer:

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Step-by-step explanation:

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