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Height of Square Pyramid given Base Angle Formula

GoHeight of Square Pyramid given Lateral Edge Length Formula

GoHeight of Square Pyramid given Volume Formula

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

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

h - Height 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?

Height of Square Pyramid given Base Angle Example

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

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

15.0425 = \sqrt{\frac{10^{2}}{4} + 16^{2} - (10 \cdot 16 \cdot \cos (70))}

15.0425m = \sqrt{\frac{{10m}^{2}}{4} + {16m}^{2} - (10m \cdot 16m \cdot \cos (70°))}

15.0425 = \sqrt{\frac{10^{2}}{4} + 16^{2} - (10 \cdot 16 \cdot \cos (70))}

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Height of Square Pyramid given Base Angle Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

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

Next Step Convert Units

∴

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

Next Step Prepare to Evaluate

∴

h = \sqrt{\frac{10^{2}}{4} + 16^{2} - (10 \cdot 16 \cdot \cos (1.2217))}

Next Step Evaluate

∴

h = 15.0424990300102m

LAST Step Rounding Answer

∴

h = 15.0425m

Height of Square Pyramid given Base Angle Formula Elements

Variables

Functions

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

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 Height of Square Pyramid

Go Height of Square Pyramid given Lateral Edge Length

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

Go Height of Square Pyramid given Volume

h = \frac{3 \cdot V}{{l e(Base)}^{2}}

Other formulas in Height of 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 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})

How to Evaluate Height of Square Pyramid given Base Angle?

Height of Square Pyramid given Base Angle evaluator 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 evaluate 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 evaluate Height of Square Pyramid given Base Angle using this online evaluator? To use this online evaluator 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.

FAQs on Height of Square Pyramid given Base Angle

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

The formula of Height of Square Pyramid given Base Angle is expressed as 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))). Here is an example- 15.0425 = sqrt((10^2)/4+16^2-(10*16*cos(1.2217304763958))).

How to calculate Height 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 Height of Square Pyramid given Base Angle using the formula - 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))). This formula also uses Cosine (cos), Square Root (sqrt) function(s).

What are the other ways to Calculate Height of Square Pyramid?

Here are the different ways to Calculate Height of Square Pyramid-

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=(3*Volume of Square Pyramid)/(Edge Length of Base of Square Pyramid^2)

Can the Height of Square Pyramid given Base Angle be negative?

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

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

Height 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 Height of Square Pyramid given Base Angle can be measured.

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Height of Square Pyramid given Base Angle Formula

​GoHeight of Square Pyramid given Lateral Edge Length Formula

​GoHeight of Square Pyramid given Volume Formula

Height of Square Pyramid given Base Angle Example

Height of Square Pyramid given Base Angle Solution

Height of Square Pyramid given Base Angle Formula Elements

Other Formulas to find Height of Square Pyramid

Other formulas in Height of Square Pyramid category

How to Evaluate Height of Square Pyramid given Base Angle?

FAQs on Height of Square Pyramid given Base Angle

Variable Name

GoHeight of Square Pyramid given Lateral Edge Length Formula

GoHeight of Square Pyramid given Volume Formula