the base of a regular pyramid is a hexagon whose perimeter is 84 feet. the volume of the pyramid is approximately 4,677.85 cubic feet. find the height of the pyramid.

The height of the pyramid is

Step-by-step explanation:

we know that

The volume of the pyramid is equal to

where

B is the area of the base of the pyramid

H is the height of the pyramid

step 1

Find the area B of the regular hexagonal base

we know that

The perimeter of a regular hexagon is

where

b is the length side of the hexagon

we have

substitute

solve for b

Remember that the area of a regular hexagon is the same that the area of six equilateral triangles

Determine the area of the six equilateral triangles, applying the formula of the law of sines

substitute the value of b

step 2

Find the height of the pyramid

we have

substitute

solve for H

we know that

applying the law of sines

°

so

∠j=18°

∠k=29°

∠l=180-(18+29)=133°

the answer part a) is

the measure of angle k is  ≈29°

part b)  the measure of angle k could also be

(180-29)=151°

so

∠j=18°

∠k=151°

∠l=180-(18+151)=11°

the answer part b) is

the measure of angle k could also be 151°

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the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: