A right pyramid with a square base has a base edge length of 12 meters and slant height of 6 meters. The apothem is meters. The
hypotenuse of ΔABC is the . The height is meters. The volume of the pyramid is cubic meters.
1 answer:
Answer:
Apothem: 6m
hypotenuse : slant height : 6√2 m
height :6m
volume: 288m2
Step-by-step explanation:
Hi, the correct values are: (image attached down below)
Base length= 12m
Slant height is actually = 6√2
So, to calculate the apothem (AC)we apply the Pythagorean theorem:
AB^2 = AC^2 + BC^2
√AB^2 -BC^2 = AC
AC = √(6√2)^2 - 6^2
AC =6 meters
Hypotenuse of ABC = AB =6√2 meters
Height = AC = 6 meters
Volume:
Volume of a pyramid = 1/3 x base area x height
area of a square = side length ^2 = 12^2
V= 1/3 x 12^2 x 6 =288 m2
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Answer: proof below
<u>Step-by-step explanation:</u>
Use the Difference formula for sin:
sin (A - B) = sin(A)·cos(B) - cos(A)·sin(B)
sin (180° - θ) = sin(180°)·cos(θ) - cos(180°)·sin(θ)
= 0 · cos(θ) - -1 · sin(θ)
= 0 - -sin(θ)
= + sin(θ)
sin (180° - θ) = sin(θ)