Mathematics, 18.01.2020 00:31 rose3358

Aregular square pyramid has base edges of length 16 and its lateral faces are inclined 30° to the base of the pyramid. what is the (1) height of the pyramid (2) volume of the pyramid?

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Answer from: dondre54

(1) 13.86 units.

(2) 1182.72 cubic units.

Step-by-step explanation:

Please find the attachment.

We have been given that a regular square pyramid has base edges of length 16 and its lateral faces are inclined 30° to the base of the pyramid.

(1) We can find height of pyramid using tan.

$\text{tan}=\frac{\text{Opposite}}{\text{Adjacent}}$

The length of opposite side will half the length of square base.

$\frac{16}{2}=8$

$\text{tan}(30^{\circ})=\frac{8}{h}$

$h=\frac{8}{\text{tan}(30^{\circ})}$

h=13.8564064605420367

$h\approx 13.86$

Therefore, the height of the pyramid will be 13.86 units.

(2). We know that volume of pyramid is 1/3 the product of base area and height.

$V=\frac{1}{3}*bh$

$V=\frac{1}{3}*16*16*13.86$

$V=\frac{1}{3}*3548.16$

V=1182.72

Therefore, the volume of the pyramid would be 1182.72 cubic units.

Aregular square pyramid has base edges of length 16 and its lateral faces are inclined 30° to the b

Answer from: Quest

the degrees would remain the same ( the number to the left of the decimal point.

the multiply the decimal by 60 to get the minutes and use the numbers to the left of the decimal point.

then multiply the decimal portion of that by 60 for the seconds and round off as needed.

39 .956652

the 39 remains the degrees.

the minutes = 0.956652 x 60 = 57.39912

the minutes = 57

the seconds = 0.39912 x 60 = 23.95 = 24 ( rounded to nearest tenth)

so 39.956652 = 39 degrees, 57 minutes and 24 seconds

-75.159809

the -75 remains the degrees

the minutes = 0.159809 x 60 = 9.58854

the minutes = 9

the seconds = 0.58854 x 60 = 35.31, rounded to nearest tenth = 35.3 seconds

so -75.159809 = -75 degrees, 9 minutes and 35.3 seconds.

the first coordinate is north or south, since it it positive it is north.

the second number is east or west, because it is negative it is west.

39 degrees, 57 minutes and 24 seconds n

-75 degrees, 9 minutes and 35.3 seconds w

Answer from: Quest

step-by-step explanation:

assume that you have 3 different side lengths. apply the pythagorean theorem here: square each of the two shortest sides; call them a and b, so that their squares are a² and b². also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.

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