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Base angle (α) of Square Pyramid Solution

STEP 0: Pre-Calculation Summary
Formula Used
angle_a = arccos((((Side A/2)^2)+(Slant Height^2)-(Height^2))/(Side A*Slant Height))
∠A = arccos((((a/2)^2)+(s^2)-(h^2))/(a*s))
This formula uses 2 Functions, 3 Variables
Functions Used
cos - Trigonometric cosine function, cos(Angle)
arccos - Inverse trigonometric cosine function, arccos(Number)
Variables Used
Side A - Side A is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back. (Measured in Meter)
Slant Height - Slant Height is the height of a cone from the vertex to the periphery (rather than the center) of the base. (Measured in Meter)
Height - Height is the distance between the lowest and highest points of a person standing upright. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Side A: 8 Meter --> 8 Meter No Conversion Required
Slant Height: 5 Meter --> 5 Meter No Conversion Required
Height: 12 Meter --> 12 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
∠A = arccos((((a/2)^2)+(s^2)-(h^2))/(a*s)) --> arccos((((8/2)^2)+(5^2)-(12^2))/(8*5))
Evaluating ... ...
∠A = NaN
STEP 3: Convert Result to Output's Unit
NaN Radian -->NaN Degree (Check conversion here)
FINAL ANSWER
NaN Degree <-- Angle A
(Calculation completed in 00.031 seconds)

11 Other formulas that you can solve using the same Inputs

Area of a Triangle when sides are given
area = sqrt((Side A+Side B+Side C)*(Side B+Side C-Side A)*(Side A-Side B+Side C)*(Side A+Side B-Side C))/4 Go
Volume of a Conical Frustum
volume = (1/3)*pi*Height*(Radius 1^2+Radius 2^2+(Radius 1*Radius 2)) Go
Total Surface Area of a Cone
total_surface_area = pi*Radius*(Radius+sqrt(Radius^2+Height^2)) Go
Lateral Surface Area of a Cone
lateral_surface_area = pi*Radius*sqrt(Radius^2+Height^2) Go
Volume of a Circular Cone
volume = (1/3)*pi*(Radius)^2*Height Go
Area of a Trapezoid
area = ((Base A+Base B)/2)*Height Go
Volume of a Circular Cylinder
volume = pi*(Radius)^2*Height Go
Volume of a Pyramid
volume = (1/3)*Side^2*Height Go
Area of a Triangle when base and height are given
area = 1/2*Base*Height Go
Area of a Parallelogram when base and height are given
area = Base*Height Go
Area of a Square when side is given
area = (Side A)^2 Go

11 Other formulas that calculate the same Output

Angle between two lines given direction cosines of that two lines w.r.to x, y & z axis
angle_a = acos ((Direction cosine with respect to x axis* Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis* Direction cosine 2 with respect to y axis)+ (Direction cosine with respect to z axis* Direction cosine 2 with respect to z axis)) Go
Angle of intersection between two circles
angle_a = arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between two origin)^2))/(2*Radius 1*Radius 2)) Go
Acute angle of a rhombus if given both diagonals
angle_a = asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2))) Go
Obtuse angle of rhombus if given both diagonal
angle_a = asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2))) Go
Acute angle of rhombus given larger diagonal and side
angle_a = (arccos(((Diagonal 1)^2)/(2*(Side of rhombus )^2))-1) Go
One-half obtuse angles in a rhombus if given both diagonals
angle_a = 2*(arctan(Diagonal 1/Diagonal 2)) Go
One-half acute angles in a rhombus if given both diagonals
angle_a = 2*(arctan(Diagonal 2/Diagonal 1)) Go
Obtuse angle of a rhombus if given area and side
angle_a = asin(Area/Side^2) Go
Acute angle of a rhombus if given area and side
angle_a = asin(Area/Side^2) Go
Angle on the remaining part of the circumference when another angle on same chord is given
angle_a = 1*Angle B Go
Angle at another point on circumference when angle on an arc is given
angle_a = 1*Angle B Go

Base angle (α) of Square Pyramid Formula

angle_a = arccos((((Side A/2)^2)+(Slant Height^2)-(Height^2))/(Side A*Slant Height))
∠A = arccos((((a/2)^2)+(s^2)-(h^2))/(a*s))

What is Square Pyramid?

In geometry, a square pyramid is a pyramid having a square base. If the apex is perpendicularly above the center of the square, it is a right square pyramid, and has C₄ᵥ symmetry. If all edges are equal, it is an equilateral square pyramid, the Johnson solid J₁

How to Calculate Base angle (α) of Square Pyramid?

Base angle (α) of Square Pyramid calculator uses angle_a = arccos((((Side A/2)^2)+(Slant Height^2)-(Height^2))/(Side A*Slant Height)) to calculate the Angle A, The Base angle (α) of Square Pyramid formula is defined as a angl e given by α = arccos( ((a/2)² + s² - h²) / (a*s) ). Where, side_a = Edge length of the base (a), s=Slant height (s). Angle A and is denoted by ∠A symbol.

How to calculate Base angle (α) of Square Pyramid using this online calculator? To use this online calculator for Base angle (α) of Square Pyramid, enter Side A (a), Slant Height (s) and Height (h) and hit the calculate button. Here is how the Base angle (α) of Square Pyramid calculation can be explained with given input values -> NaN = arccos((((8/2)^2)+(5^2)-(12^2))/(8*5)).

FAQ

What is Base angle (α) of Square Pyramid?
The Base angle (α) of Square Pyramid formula is defined as a angl e given by α = arccos( ((a/2)² + s² - h²) / (a*s) ). Where, side_a = Edge length of the base (a), s=Slant height (s) and is represented as ∠A = arccos((((a/2)^2)+(s^2)-(h^2))/(a*s)) or angle_a = arccos((((Side A/2)^2)+(Slant Height^2)-(Height^2))/(Side A*Slant Height)). Side A is an upright or sloping surface of a structure or object that is not the top or bottom and generally not the front or back, Slant Height is the height of a cone from the vertex to the periphery (rather than the center) of the base and Height is the distance between the lowest and highest points of a person standing upright.
How to calculate Base angle (α) of Square Pyramid?
The Base angle (α) of Square Pyramid formula is defined as a angl e given by α = arccos( ((a/2)² + s² - h²) / (a*s) ). Where, side_a = Edge length of the base (a), s=Slant height (s) is calculated using angle_a = arccos((((Side A/2)^2)+(Slant Height^2)-(Height^2))/(Side A*Slant Height)). To calculate Base angle (α) of Square Pyramid, you need Side A (a), Slant Height (s) and Height (h). With our tool, you need to enter the respective value for Side A, Slant Height and Height and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Angle A?
In this formula, Angle A uses Side A, Slant Height and Height. We can use 11 other way(s) to calculate the same, which is/are as follows -
  • angle_a = 1*Angle B
  • angle_a = 1*Angle B
  • angle_a = (arccos(((Diagonal 1)^2)/(2*(Side of rhombus )^2))-1)
  • angle_a = arccos((((Radius 1)^2)+((Radius 2)^2)-((Distance between two origin)^2))/(2*Radius 1*Radius 2))
  • angle_a = asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2)))
  • angle_a = asin((2*Diagonal 1*Diagonal 2)/((Diagonal 1^2)+(Diagonal 2^2)))
  • angle_a = asin(Area/Side^2)
  • angle_a = asin(Area/Side^2)
  • angle_a = 2*(arctan(Diagonal 2/Diagonal 1))
  • angle_a = 2*(arctan(Diagonal 1/Diagonal 2))
  • angle_a = acos ((Direction cosine with respect to x axis* Direction cosine 2 with respect to x axis)+(Direction cosine with respect to y axis* Direction cosine 2 with respect to y axis)+ (Direction cosine with respect to z axis* Direction cosine 2 with respect to z axis))
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