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Long Diagonal of Trapezoid given Long Leg Formula

GoLong Diagonal of Trapezoid Formula

GoLong Diagonal of Trapezoid given all Sides 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{{B Short}^{2} + {L Long}^{2} - (2 \cdot B Short \cdot L Long \cdot \cos (∠ Larger Obtuse))}

d_Long - Long Diagonal of Trapezoid?B_Short - Short Base of Trapezoid?L_Long - Long Leg of Trapezoid?∠_{Larger Obtuse} - Larger Obtuse Angle of Trapezoid?

Long Diagonal of Trapezoid given Long Leg Example

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

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

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

14.721 = \sqrt{5^{2} + 11^{2} - (2 \cdot 5 \cdot 11 \cdot \cos (130))}

14.721m = \sqrt{{5m}^{2} + {11m}^{2} - (2 \cdot 5m \cdot 11m \cdot \cos (130°))}

14.721 = \sqrt{5^{2} + 11^{2} - (2 \cdot 5 \cdot 11 \cdot \cos (130))}

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Long Diagonal of Trapezoid given Long Leg Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Long = \sqrt{{5m}^{2} + {11m}^{2} - (2 \cdot 5m \cdot 11m \cdot \cos (130°))}

Next Step Convert Units

∴

d Long = \sqrt{{5m}^{2} + {11m}^{2} - (2 \cdot 5m \cdot 11m \cdot \cos (2.2689rad))}

Next Step Prepare to Evaluate

∴

d Long = \sqrt{5^{2} + 11^{2} - (2 \cdot 5 \cdot 11 \cdot \cos (2.2689))}

Next Step Evaluate

∴

d Long = 14.7209591082063m

LAST Step Rounding Answer

∴

d Long = 14.721m

Long Diagonal of Trapezoid given Long Leg 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

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

Long Leg of Trapezoid

Long Leg of Trapezoid is the longer side among the pair of non parallel and opposite sides of the Trapezoid.

Symbol: L_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Leg of Trapezoid

Larger Obtuse Angle of Trapezoid

Larger Obtuse Angle of Trapezoid is the larger angle on the short base or the angle made by the short base and long leg of the Trapezoid.

Symbol: ∠_{Larger Obtuse}

Measurement: AngleUnit: °

Note: Value should be between 90 to 180.

Formulas to find Larger Obtuse Angle of Trapezoid

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 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 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}}

Go Long Diagonal of Trapezoid given Height

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

How to Evaluate Long Diagonal of Trapezoid given Long Leg?

Long Diagonal of Trapezoid given Long Leg evaluator uses 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))) to evaluate the Long Diagonal of Trapezoid, Long Diagonal of Trapezoid given Long Leg 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 long leg of the Trapezoid. Long Diagonal of Trapezoid is denoted by d_Long symbol.

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

FAQs on Long Diagonal of Trapezoid given Long Leg

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

The formula of Long Diagonal of Trapezoid given Long Leg is expressed as 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))). Here is an example- 14.72096 = sqrt(5^2+11^2-(2*5*11*cos(2.2689280275922))).

How to calculate Long Diagonal of Trapezoid given Long Leg?

With Short Base of Trapezoid (B_Short), Long Leg of Trapezoid (L_Long) & Larger Obtuse Angle of Trapezoid (∠_{Larger Obtuse}) we can find Long Diagonal of Trapezoid given Long Leg using the formula - 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))). This formula also uses Cosine (cos), 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 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)))
Long Diagonal of Trapezoid=sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2)

Can the Long Diagonal of Trapezoid given Long Leg be negative?

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

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

Long Diagonal of Trapezoid given Long Leg 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 Long Leg can be measured.

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Long Diagonal of Trapezoid given Long Leg Formula

​GoLong Diagonal of Trapezoid Formula

​GoLong Diagonal of Trapezoid given all Sides Formula

Long Diagonal of Trapezoid given Long Leg Example

Long Diagonal of Trapezoid given Long Leg Solution

Long Diagonal of Trapezoid given Long Leg Formula Elements

Other Formulas to find Long Diagonal of Trapezoid

How to Evaluate Long Diagonal of Trapezoid given Long Leg?

FAQs on Long Diagonal of Trapezoid given Long Leg

Variable Name

GoLong Diagonal of Trapezoid Formula

GoLong Diagonal of Trapezoid given all Sides Formula