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Y_Kistochka [10]
3 years ago
5

The Great Pyramids of Giza are named the Pyramid of Menkaure, the Pyramid of Khafre and the Pyramid of Khufu. The height and bas

e of each of these pyramids are: 65.5 m by 103.4 m2, 136.4 m by 215.25 m2, 138.8 m by 230.4 m2 respectively. What is the volume of each of the Great Pyramids of Giza?
Mathematics
1 answer:
mihalych1998 [28]3 years ago
8 0

Step-by-step explanation:

The volume of a pyramid is equal to one third the product of the area of the base and the height.

Pyramid of Menkaure

Area of Base, B = 103.4 m2

Height, H = 65.5 m

Volume = 1/3 * BH

Volume = 1/3 * 103.4 * 65.5 = 2257.56 m3

Pyramid of Khafre

Area of Base, B = 215.25 m2

Height, H = 136.4 m

Volume = 1/3 * BH

Volume = 1/3 * 215.25 * 136.4 = 9786.7 m3

Pyramid of Khufu

Area of Base, B = 230.4 m2

Height, H = 138.8 m

Volume = 1/3 * BH

Volume = 1/3 * 230.4 * 138.8 = 10598.4 m3

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Answer: Choice C) 2

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Explanation:

Using the law of sines, we get
sin(B)/b = sin(C)/c
sin(18)/7 = sin(C)/11
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11*0.0441452849107 = sin(C)
0.4855981340177 = sin(C)
sin(C) = 0.4855981340177
C = arcsin(0.4855981340177) or C = 180-arcsin(0.4855981340177)
C = 29.0516679549861 or C = 150.948332045013
There are two possibilities for angle C because of something like sin(30) = sin(150) = 1/2 = 0.5

Those approximate values of C round to
C = 29.05 and C = 150.95

If C = 29.05, then angle A is
A = 180-B-C
A = 180-18-29.05
A = 132.95
Making this triangle possible since angle A is a positive number

If C = 150.95, then angle A is 
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A = 180-18-150.95
A = 11.05
making this triangle possible since angle A is a positive number

There are two distinct triangles that can be formed. 
One triangle is with the angles: A = 132.95, B = 18, C = 29.05
The other triangle is with the angles: A = 11.05, B = 18, C = 150.95
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Answer:

x needs to be smaller or equal to -3

Step-by-step explanation:

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