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Long Diagonal of Trapezoid given Height Formula

GoLong Diagonal of Trapezoid Formula

GoLong Diagonal of Trapezoid given Long Leg Formula

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Long Diagonal of Trapezoid is the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid. Check FAQs

d Long = \sqrt{h^{2} + {(B Short + (h \cdot \cot (∠ Smaller Acute)))}^{2}}

d_Long - Long Diagonal of Trapezoid?h - Height of Trapezoid?B_Short - Short Base of Trapezoid?∠_{Smaller Acute} - Smaller Acute Angle of Trapezoid?

Long Diagonal of Trapezoid given Height Example

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Here is how the Long Diagonal of Trapezoid given Height equation looks like with Values.

Here is how the Long Diagonal of Trapezoid given Height equation looks like with Units.

Here is how the Long Diagonal of Trapezoid given Height equation looks like.

14.1841 = \sqrt{8^{2} + {(5 + (8 \cdot \cot (50)))}^{2}}

14.1841m = \sqrt{{8m}^{2} + {(5m + (8m \cdot \cot (50°)))}^{2}}

14.1841 = \sqrt{8^{2} + {(5 + (8 \cdot \cot (50)))}^{2}}

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Long Diagonal of Trapezoid given Height Solution

Follow our step by step solution on how to calculate Long Diagonal of Trapezoid given Height?

FIRST Step Consider the formula

d Long = \sqrt{h^{2} + {(B Short + (h \cdot \cot (∠ Smaller Acute)))}^{2}}

Next Step Substitute values of Variables

∴

d Long = \sqrt{{8m}^{2} + {(5m + (8m \cdot \cot (50°)))}^{2}}

Next Step Convert Units

∴

d Long = \sqrt{{8m}^{2} + {(5m + (8m \cdot \cot (0.8727rad)))}^{2}}

Next Step Prepare to Evaluate

∴

d Long = \sqrt{8^{2} + {(5 + (8 \cdot \cot (0.8727)))}^{2}}

Next Step Evaluate

∴

d Long = 14.1841324980033m

LAST Step Rounding Answer

∴

d Long = 14.1841m

Long Diagonal of Trapezoid given Height Formula Elements

Variables

Functions

Long Diagonal of Trapezoid

Long Diagonal of Trapezoid is the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid.

Symbol: d_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Diagonal of Trapezoid

Height of Trapezoid

Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Trapezoid

Short Base of Trapezoid

Short Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid.

Symbol: B_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Base of Trapezoid

Smaller Acute Angle of Trapezoid

Smaller Acute Angle of Trapezoid is the smaller angle on the long base or the angle made by the long base and long leg of the Trapezoid.

Symbol: ∠_{Smaller Acute}

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Smaller Acute Angle of Trapezoid

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(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 Long Diagonal of Trapezoid

Go Long Diagonal of Trapezoid

d Long = \sqrt{{B Long}^{2} + {L Short}^{2} - (2 \cdot B Long \cdot L Short \cdot \cos (∠ Larger Acute))}

Go Long Diagonal of Trapezoid given Long Leg

d Long = \sqrt{{B Short}^{2} + {L Long}^{2} - (2 \cdot B Short \cdot L Long \cdot \cos (∠ Larger Obtuse))}

Go Long Diagonal of Trapezoid given all Sides

d Long = \sqrt{{L Short}^{2} + (B Short \cdot B Long) - (B Long \cdot \frac{{L Short}^{2} - {L Long}^{2}}{B Long - B Short})}

Go Long Diagonal of Trapezoid given Height and Larger Acute Angle

d Long = \sqrt{h^{2} + {(B Long - (h \cdot \cot (∠ Larger Acute)))}^{2}}

How to Evaluate Long Diagonal of Trapezoid given Height?

Long Diagonal of Trapezoid given Height evaluator uses Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2) to evaluate the Long Diagonal of Trapezoid, Long Diagonal of Trapezoid given Height formula is defined as the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid, and calculated using height of the Trapezoid. Long Diagonal of Trapezoid is denoted by d_Long symbol.

How to evaluate Long Diagonal of Trapezoid given Height using this online evaluator? To use this online evaluator for Long Diagonal of Trapezoid given Height, enter Height of Trapezoid (h), Short Base of Trapezoid (B_Short) & Smaller Acute Angle of Trapezoid (∠_{Smaller Acute}) and hit the calculate button.

FAQs on Long Diagonal of Trapezoid given Height

What is the formula to find Long Diagonal of Trapezoid given Height?

The formula of Long Diagonal of Trapezoid given Height is expressed as Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2). Here is an example- 14.18413 = sqrt(8^2+(5+(8*cot(0.872664625997001)))^2).

How to calculate Long Diagonal of Trapezoid given Height?

With Height of Trapezoid (h), Short Base of Trapezoid (B_Short) & Smaller Acute Angle of Trapezoid (∠_{Smaller Acute}) we can find Long Diagonal of Trapezoid given Height using the formula - Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2). This formula also uses Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Long Diagonal of Trapezoid?

Here are the different ways to Calculate Long Diagonal of Trapezoid-

Long Diagonal of Trapezoid=sqrt(Long Base of Trapezoid^2+Short Leg of Trapezoid^2-(2*Long Base of Trapezoid*Short Leg of Trapezoid*cos(Larger Acute Angle of Trapezoid)))
Long Diagonal of Trapezoid=sqrt(Short Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Short Base of Trapezoid*Long Leg of Trapezoid*cos(Larger Obtuse Angle of Trapezoid)))
Long Diagonal of Trapezoid=sqrt(Short Leg of Trapezoid^2+(Short Base of Trapezoid*Long Base of Trapezoid)-(Long Base of Trapezoid*(Short Leg of Trapezoid^2-Long Leg of Trapezoid^2)/(Long Base of Trapezoid-Short Base of Trapezoid)))

Can the Long Diagonal of Trapezoid given Height be negative?

No, the Long Diagonal of Trapezoid given Height, measured in Length cannot be negative.

Which unit is used to measure Long Diagonal of Trapezoid given Height?

Long Diagonal of Trapezoid given Height is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Long Diagonal of Trapezoid given Height can be measured.

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Long Diagonal of Trapezoid given Height Formula

​GoLong Diagonal of Trapezoid Formula

​GoLong Diagonal of Trapezoid given Long Leg Formula

Long Diagonal of Trapezoid given Height Example

Long Diagonal of Trapezoid given Height Solution

Long Diagonal of Trapezoid given Height Formula Elements

Other Formulas to find Long Diagonal of Trapezoid

How to Evaluate Long Diagonal of Trapezoid given Height?

FAQs on Long Diagonal of Trapezoid given Height

Variable Name

GoLong Diagonal of Trapezoid Formula

GoLong Diagonal of Trapezoid given Long Leg Formula