Height 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%

✖Height of Square Pyramid is the length of the perpendicular from the apex to the base of the Square Pyramid.ⓘ Height of Square Pyramid given Base Angle [h]

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Height of Square Pyramid given Base Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height 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*Slant Height of Square Pyramid*cos(Base Angle of Square Pyramid)))
h = sqrt((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

Height of Square Pyramid - (Measured in Meter) - Height of Square Pyramid is the length of the perpendicular from the apex to the base 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

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

Evaluating ... ...

h = 15.0424990300102

STEP 3: Convert Result to Output's Unit

15.0424990300102 Meter --> No Conversion Required

FINAL ANSWER

15.0424990300102 ≈ 15.0425 Meter <-- Height of Square Pyramid

(Calculation completed in 00.004 seconds)

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Walchand College of Engineering (WCE), Sangli

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< Height of Square Pyramid Calculators

Height of Square Pyramid given Base Angle

LaTeX Go Height 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*Slant Height of Square Pyramid*cos(Base Angle of Square Pyramid)))

Height of Square Pyramid given Total Surface Area

LaTeX Go Height of Square Pyramid = sqrt((((Total Surface Area of Square Pyramid-Edge Length of Base of Square Pyramid^2)/Edge Length of Base of Square Pyramid)^2-Edge Length of Base of Square Pyramid^2)/4)

Height of Square Pyramid given Lateral Edge Length

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

Height of Square Pyramid given Slant Height

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

< 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

Height 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 Height of Square Pyramid given Base Angle?

Height of Square Pyramid given Base Angle calculator uses Height 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*Slant Height of Square Pyramid*cos(Base Angle of Square Pyramid))) to calculate the Height of Square Pyramid, Height of Square Pyramid given Base Angle formula is defined as the length of the perpendicular from the apex to the base of the Square Pyramid and is calculated using the base angle of the Square Pyramid. Height of Square Pyramid is denoted by h symbol.

How to calculate Height of Square Pyramid given Base Angle using this online calculator? To use this online calculator for Height 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 Height of Square Pyramid given Base Angle calculation can be explained with given input values -> 15.0425 = sqrt((10^2)/4+16^2-(10*16*cos(1.2217304763958))).

FAQ

What is Height of Square Pyramid given Base Angle?

Height of Square Pyramid given Base Angle formula is defined as the length of the perpendicular from the apex to the base of the Square Pyramid and is calculated using the base angle of the Square Pyramid and is represented as h = sqrt((l_e(Base)^2)/4+h_slant^2-(l_e(Base)*h_slant*cos(∠_Base))) or Height 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*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 Height of Square Pyramid given Base Angle?

Height of Square Pyramid given Base Angle formula is defined as the length of the perpendicular from the apex to the base of the Square Pyramid and is calculated using the base angle of the Square Pyramid is calculated using Height 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*Slant Height of Square Pyramid*cos(Base Angle of Square Pyramid))). To calculate Height 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 Height of Square Pyramid?

In this formula, Height 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 -

Height of Square Pyramid = sqrt((((Total Surface Area of Square Pyramid-Edge Length of Base of Square Pyramid^2)/Edge Length of Base of Square Pyramid)^2-Edge Length of Base of Square Pyramid^2)/4)
Height of Square Pyramid = sqrt(Slant Height of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/4)
Height of Square Pyramid = sqrt(Lateral Edge Length of Square Pyramid^2-(Edge Length of Base of Square Pyramid^2)/2)

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