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Lateral Edge Length of Square Pyramid given Base Angle Formula

GoLateral Edge Length of Square Pyramid Formula

GoLateral Edge Length of Square Pyramid given Volume and Height Formula

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Lateral Edge Length of Square Pyramid is the length of the straight line connecting any base vertex to the apex of the Square Pyramid. Check FAQs

l e(Lateral) = \sqrt{\frac{3 \cdot {l e(Base)}^{2}}{4} + {h slant}^{2} - (l e(Base) \cdot h slant \cdot \cos (∠ Base))}

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

Lateral Edge Length of Square Pyramid given Base Angle Example

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Here is how the Lateral Edge Length of Square Pyramid given Base Angle equation looks like with Values.

Here is how the Lateral Edge Length of Square Pyramid given Base Angle equation looks like with Units.

Here is how the Lateral Edge Length of Square Pyramid given Base Angle equation looks like.

16.6216 = \sqrt{\frac{3 \cdot 10^{2}}{4} + 16^{2} - (10 \cdot 16 \cdot \cos (70))}

16.6216m = \sqrt{\frac{3 \cdot {10m}^{2}}{4} + {16m}^{2} - (10m \cdot 16m \cdot \cos (70°))}

16.6216 = \sqrt{\frac{3 \cdot 10^{2}}{4} + 16^{2} - (10 \cdot 16 \cdot \cos (70))}

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Lateral Edge Length of Square Pyramid given Base Angle Solution

Follow our step by step solution on how to calculate Lateral Edge Length of Square Pyramid given Base Angle?

FIRST Step Consider the formula

l e(Lateral) = \sqrt{\frac{3 \cdot {l e(Base)}^{2}}{4} + {h slant}^{2} - (l e(Base) \cdot h slant \cdot \cos (∠ Base))}

Next Step Substitute values of Variables

∴

l e(Lateral) = \sqrt{\frac{3 \cdot {10m}^{2}}{4} + {16m}^{2} - (10m \cdot 16m \cdot \cos (70°))}

Next Step Convert Units

∴

l e(Lateral) = \sqrt{\frac{3 \cdot {10m}^{2}}{4} + {16m}^{2} - (10m \cdot 16m \cdot \cos (1.2217rad))}

Next Step Prepare to Evaluate

∴

l e(Lateral) = \sqrt{\frac{3 \cdot 10^{2}}{4} + 16^{2} - (10 \cdot 16 \cdot \cos (1.2217))}

Next Step Evaluate

∴

l e(Lateral) = 16.6215756493739m

LAST Step Rounding Answer

∴

l e(Lateral) = 16.6216m

Lateral Edge Length of Square Pyramid given Base Angle Formula Elements

Variables

Functions

Lateral Edge Length of Square Pyramid

Lateral Edge Length of Square Pyramid is the length of the straight line connecting any base vertex to the apex of the Square Pyramid.

Symbol: l_e(Lateral)

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Lateral Edge Length 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

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

cos

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

Syntax: cos(Angle)

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other Formulas to find Lateral Edge Length of Square Pyramid

Go Lateral Edge Length of Square Pyramid

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

Go Lateral Edge Length of Square Pyramid given Volume and Height

l e(Lateral) = \sqrt{h^{2} + (\frac{3}{2} \cdot \frac{V}{h})}

Other formulas in Edge Length of Square Pyramid category

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 Base Angle of Square Pyramid

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

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 Lateral Edge Length of Square Pyramid given Base Angle?

Lateral Edge Length of Square Pyramid given Base Angle evaluator uses Lateral Edge Length of Square Pyramid = sqrt((3*Edge Length of Base of Square Pyramid^2)/4+Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid*cos(Base Angle of Square Pyramid))) to evaluate the Lateral Edge Length of Square Pyramid, Lateral Edge Length of Square Pyramid given Base Angle formula is defined as the length of the straight line connecting any base vertex to the apex of the Square Pyramid and is calculated using the base angle of the Square Pyramid. Lateral Edge Length of Square Pyramid is denoted by l_e(Lateral) symbol.

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

FAQs on Lateral Edge Length of Square Pyramid given Base Angle

What is the formula to find Lateral Edge Length of Square Pyramid given Base Angle?

The formula of Lateral Edge Length of Square Pyramid given Base Angle is expressed as Lateral Edge Length of Square Pyramid = sqrt((3*Edge Length of Base of Square Pyramid^2)/4+Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid*cos(Base Angle of Square Pyramid))). Here is an example- 16.62158 = sqrt((3*10^2)/4+16^2-(10*16*cos(1.2217304763958))).

How to calculate Lateral Edge Length of Square Pyramid given Base Angle?

With Edge Length of Base of Square Pyramid (l_e(Base)), Slant Height of Square Pyramid (h_slant) & Base Angle of Square Pyramid (∠_Base) we can find Lateral Edge Length of Square Pyramid given Base Angle using the formula - Lateral Edge Length of Square Pyramid = sqrt((3*Edge Length of Base of Square Pyramid^2)/4+Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid*Slant Height of Square Pyramid*cos(Base Angle of Square Pyramid))). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Lateral Edge Length of Square Pyramid?

Here are the different ways to Calculate Lateral Edge Length of Square Pyramid-

Lateral Edge Length of Square Pyramid=sqrt(Edge Length of Base of Square Pyramid^2/2+Height of Square Pyramid^2)
Lateral Edge Length of Square Pyramid=sqrt(Height of Square Pyramid^2+(3/2*Volume of Square Pyramid/Height of Square Pyramid))

Can the Lateral Edge Length of Square Pyramid given Base Angle be negative?

No, the Lateral Edge Length of Square Pyramid given Base Angle, measured in Length cannot be negative.

Which unit is used to measure Lateral Edge Length of Square Pyramid given Base Angle?

Lateral Edge Length of Square Pyramid given Base Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Lateral Edge Length of Square Pyramid given Base Angle can be measured.

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Lateral Edge Length of Square Pyramid given Base Angle Formula

​GoLateral Edge Length of Square Pyramid Formula

​GoLateral Edge Length of Square Pyramid given Volume and Height Formula

Lateral Edge Length of Square Pyramid given Base Angle Example

Lateral Edge Length of Square Pyramid given Base Angle Solution

Lateral Edge Length of Square Pyramid given Base Angle Formula Elements

Other Formulas to find Lateral Edge Length of Square Pyramid

Other formulas in Edge Length of Square Pyramid category

How to Evaluate Lateral Edge Length of Square Pyramid given Base Angle?

FAQs on Lateral Edge Length of Square Pyramid given Base Angle

Variable Name

GoLateral Edge Length of Square Pyramid Formula

GoLateral Edge Length of Square Pyramid given Volume and Height Formula