Lateral Edge Length of Square Pyramid given Base Angle Calculator

✖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.ⓘ Edge Length of Base of Square Pyramid [l_e(Base)]			+10% -10%
✖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.ⓘ Slant Height of Square Pyramid [h_slant]			+10% -10%
✖Base Angle of Square Pyramid is the angle between any of the joining triangular faces and the base square face of the Square Pyramid.ⓘ Base Angle of Square Pyramid [∠_Base]			+10% -10%

✖Lateral Edge Length of Square Pyramid is the length of the straight line connecting any base vertex to the apex of the Square Pyramid.ⓘ Lateral Edge Length of Square Pyramid given Base Angle [l_e(Lateral)]

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Lateral Edge Length of Square Pyramid given Base Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
l_e(Lateral) = sqrt((3*l_e(Base)^2)/4+h_slant^2-(l_e(Base)*h_slant*cos(∠_Base)))
This formula uses 2 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., sqrt(Number)

Variables Used

Lateral Edge Length of Square Pyramid - (Measured in Meter) - Lateral Edge Length of Square Pyramid is the length of the straight line connecting any base vertex to the apex of the Square Pyramid.
Edge Length of Base of Square Pyramid - (Measured in Meter) - 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.
Slant Height of Square Pyramid - (Measured in Meter) - 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.
Base Angle of Square Pyramid - (Measured in Radian) - Base Angle of Square Pyramid is the angle between any of the joining triangular faces and the base square face of the Square Pyramid.

STEP 1: Convert Input(s) to Base Unit

Edge Length of Base of Square Pyramid: 10 Meter --> 10 Meter No Conversion Required
Slant Height of Square Pyramid: 16 Meter --> 16 Meter No Conversion Required
Base Angle of Square Pyramid: 70 Degree --> 1.2217304763958 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

l_e(Lateral) = sqrt((3*l_e(Base)^2)/4+h_slant^2-(l_e(Base)*h_slant*cos(∠_Base))) --> sqrt((3*10^2)/4+16^2-(10*16*cos(1.2217304763958)))

Evaluating ... ...

l_e(Lateral) = 16.6215756493739

STEP 3: Convert Result to Output's Unit

16.6215756493739 Meter --> No Conversion Required

FINAL ANSWER

16.6215756493739 ≈ 16.62158 Meter <-- Lateral Edge Length of Square Pyramid

(Calculation completed in 00.004 seconds)

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< Edge Length of Square Pyramid Calculators

Lateral Edge Length of Square Pyramid given Slant Height

LaTeX Go Lateral Edge Length of Square Pyramid = sqrt((Edge Length of Base of Square Pyramid^2)/4+Slant Height of Square Pyramid^2)

Edge Length of Base of Square Pyramid given Lateral Edge Length

LaTeX Go Edge Length of Base of Square Pyramid = sqrt(2*(Lateral Edge Length of Square Pyramid^2-Height of Square Pyramid^2))

Lateral Edge Length of Square Pyramid

LaTeX Go Lateral Edge Length of Square Pyramid = sqrt(Edge Length of Base of Square Pyramid^2/2+Height of Square Pyramid^2)

Edge Length of Base of Square Pyramid given Slant Height

LaTeX Go Edge Length of Base of Square Pyramid = 2*sqrt(Slant Height of Square Pyramid^2-Height of Square Pyramid^2)

< Important Formulas of Regular Square Pyramid Calculators

Base Angle of Square Pyramid

LaTeX Go 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))

Lateral Edge Length of Square Pyramid

LaTeX Go Lateral Edge Length of Square Pyramid = sqrt(Edge Length of Base of Square Pyramid^2/2+Height of Square Pyramid^2)

Slant Height of Square Pyramid

LaTeX Go Slant Height of Square Pyramid = sqrt((Edge Length of Base of Square Pyramid^2)/4+Height of Square Pyramid^2)

Base Area of Square Pyramid

LaTeX Go Base Area of Square Pyramid = Edge Length of Base of Square Pyramid^2

Lateral Edge Length of Square Pyramid given Base Angle Formula

LaTeX Go

What is a Square Pyramid?

A Square Pyramid is a pyramid with a square base and four isosceles triangular faces that intersect at a point in geometry (the apex). It has 5 faces, which include 4 isosceles triangular faces, and a square base. Also, It has 5 vertices and 8 edges.

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

Lateral Edge Length of Square Pyramid given Base Angle calculator 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 calculate 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 calculate Lateral Edge Length of Square Pyramid given Base Angle using this online calculator? To use this online calculator 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. Here is how the Lateral Edge Length of Square Pyramid given Base Angle calculation can be explained with given input values -> 16.62158 = sqrt((3*10^2)/4+16^2-(10*16*cos(1.2217304763958))).

FAQ

What is Lateral Edge Length of Square Pyramid given Base Angle?

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 and is represented as l_e(Lateral) = sqrt((3*l_e(Base)^2)/4+h_slant^2-(l_e(Base)*h_slant*cos(∠_Base))) or 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))). 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, 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 & Base Angle of Square Pyramid is the angle between any of the joining triangular faces and the base square face of the Square Pyramid.

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

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 is calculated using 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 calculate Lateral Edge Length of Square Pyramid given Base Angle, you need Edge Length of Base of Square Pyramid (l_e(Base)), Slant Height of Square Pyramid (h_slant) & Base Angle of Square Pyramid (∠_Base). With our tool, you need to enter the respective value for Edge Length of Base of Square Pyramid, Slant Height of Square Pyramid & Base Angle of Square Pyramid 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 Lateral Edge Length of Square Pyramid?

In this formula, Lateral Edge Length of Square Pyramid uses Edge Length of Base of Square Pyramid, Slant Height of Square Pyramid & Base Angle of Square Pyramid. We can use 3 other way(s) to calculate the same, which is/are as follows -

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((Edge Length of Base of Square Pyramid^2)/4+Slant Height of Square Pyramid^2)
Lateral Edge Length of Square Pyramid = sqrt((2*Slant Height of Square Pyramid^2)-Height of Square Pyramid^2)

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