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Base Angle of Square Pyramid Formula

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Base Angle of Square Pyramid is the angle between any of the joining triangular faces and the base square face of the Square Pyramid. Check FAQs

∠ Base = \arccos (\frac{{(\frac{l e(Base)}{2})}^{2} + {h slant}^{2} - h^{2}}{l e(Base) \cdot h slant})

∠_Base - Base Angle of Square Pyramid?l_e(Base) - Edge Length of Base of Square Pyramid?h_slant - Slant Height of Square Pyramid?h - Height of Square Pyramid?

Base Angle of Square Pyramid Example

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Here is how the Base Angle of Square Pyramid equation looks like with Values.

Here is how the Base Angle of Square Pyramid equation looks like with Units.

Here is how the Base Angle of Square Pyramid equation looks like.

69.5127 = \arccos (\frac{{(\frac{10}{2})}^{2} + 16^{2} - 15^{2}}{10 \cdot 16})

69.5127° = \arccos (\frac{{(\frac{10m}{2})}^{2} + {16m}^{2} - {15m}^{2}}{10m \cdot 16m})

69.5127 = \arccos (\frac{{(\frac{10}{2})}^{2} + 16^{2} - 15^{2}}{10 \cdot 16})

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Base Angle of Square Pyramid Solution

Follow our step by step solution on how to calculate Base Angle of Square Pyramid?

FIRST Step Consider the formula

∠ Base = \arccos (\frac{{(\frac{l e(Base)}{2})}^{2} + {h slant}^{2} - h^{2}}{l e(Base) \cdot h slant})

Next Step Substitute values of Variables

∴

∠ Base = \arccos (\frac{{(\frac{10m}{2})}^{2} + {16m}^{2} - {15m}^{2}}{10m \cdot 16m})

Next Step Prepare to Evaluate

∴

∠ Base = \arccos (\frac{{(\frac{10}{2})}^{2} + 16^{2} - 15^{2}}{10 \cdot 16})

Next Step Evaluate

∴

∠ Base = 1.21322522314939rad

Next Step Convert to Output's Unit

∴

∠ Base = 69.5126848852904°

LAST Step Rounding Answer

∴

∠ Base = 69.5127°

Base Angle of Square Pyramid Formula Elements

Variables

Functions

Base Angle of Square Pyramid

Base Angle of Square Pyramid is the angle between any of the joining triangular faces and the base square face of the Square Pyramid.

Symbol: ∠_Base

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Base Angle of Square Pyramid

Edge Length of Base of Square Pyramid

Edge Length of Base of Square Pyramid is the length of the straight line connecting any two adjacent vertices of the base of the Square Pyramid.

Symbol: l_e(Base)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Edge Length of Base of Square Pyramid

Slant Height of Square Pyramid

Slant Height of Square Pyramid is the length measured along the lateral face from the base to the apex of the Square Pyramid along the center of the face.

Symbol: h_slant

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Slant Height of Square Pyramid

Height of Square Pyramid

Height of Square Pyramid is the length of the perpendicular from the apex to the base of the Square Pyramid.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Square Pyramid

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

arccos

Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio.

Syntax: arccos(Number)

Other formulas in Regular Square Pyramid category

Go Lateral Edge Length of Square Pyramid

l e(Lateral) = \sqrt{\frac{{l e(Base)}^{2}}{2} + h^{2}}

Go Slant Height of Square Pyramid

h slant = \sqrt{\frac{{l e(Base)}^{2}}{4} + h^{2}}

Go Base Area of Square Pyramid

A Base = {l e(Base)}^{2}

Go Edge Length of Base of Square Pyramid given Lateral Edge Length

l e(Base) = \sqrt{2 \cdot ({l e(Lateral)}^{2} - h^{2})}

How to Evaluate Base Angle of Square Pyramid?

Base Angle of Square Pyramid evaluator uses Base Angle of Square Pyramid = arccos(((Edge Length of Base of Square Pyramid/2)^2+Slant Height of Square Pyramid^2-Height of Square Pyramid^2)/(Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid)) to evaluate the Base Angle of Square Pyramid, Base Angle of Square Pyramid formula is defined as the angle between any of the joining faces and the base face of the Square Pyramid. Base Angle of Square Pyramid is denoted by ∠_Base symbol.

How to evaluate Base Angle of Square Pyramid using this online evaluator? To use this online evaluator for Base Angle of Square Pyramid, enter Edge Length of Base of Square Pyramid (l_e(Base)), Slant Height of Square Pyramid (h_slant) & Height of Square Pyramid (h) and hit the calculate button.

FAQs on Base Angle of Square Pyramid

What is the formula to find Base Angle of Square Pyramid?

The formula of Base Angle of Square Pyramid is expressed as Base Angle of Square Pyramid = arccos(((Edge Length of Base of Square Pyramid/2)^2+Slant Height of Square Pyramid^2-Height of Square Pyramid^2)/(Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid)). Here is an example- 3982.783 = arccos(((10/2)^2+16^2-15^2)/(10*16)).

How to calculate Base Angle of Square Pyramid?

With Edge Length of Base of Square Pyramid (l_e(Base)), Slant Height of Square Pyramid (h_slant) & Height of Square Pyramid (h) we can find Base Angle of Square Pyramid using the formula - Base Angle of Square Pyramid = arccos(((Edge Length of Base of Square Pyramid/2)^2+Slant Height of Square Pyramid^2-Height of Square Pyramid^2)/(Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid)). This formula also uses Cosine, Inverse Cosine function(s).

Can the Base Angle of Square Pyramid be negative?

No, the Base Angle of Square Pyramid, measured in Angle cannot be negative.

Which unit is used to measure Base Angle of Square Pyramid?

Base Angle of Square Pyramid is usually measured using the Degree[°] for Angle. Radian[°], Minute[°], Second[°] are the few other units in which Base Angle of Square Pyramid can be measured.

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Base Angle of Square Pyramid Formula

Base Angle of Square Pyramid Example

Base Angle of Square Pyramid Solution

Base Angle of Square Pyramid Formula Elements

Other formulas in Regular Square Pyramid category

How to Evaluate Base Angle of Square Pyramid?

FAQs on Base Angle of Square Pyramid

Variable Name