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Long Diagonal of Trapezoid Formula

GoLong Diagonal of Trapezoid given all Sides Formula

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

d_Long - Long Diagonal of Trapezoid?B_Long - Long Base of Trapezoid?L_Short - Short Leg of Trapezoid?∠_{Larger Acute} - Larger Acute Angle of Trapezoid?

Long Diagonal of Trapezoid Example

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

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

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

14.6169 = \sqrt{15^{2} + 9^{2} - (2 \cdot 15 \cdot 9 \cdot \cos (70))}

14.6169m = \sqrt{{15m}^{2} + {9m}^{2} - (2 \cdot 15m \cdot 9m \cdot \cos (70°))}

14.6169 = \sqrt{15^{2} + 9^{2} - (2 \cdot 15 \cdot 9 \cdot \cos (70))}

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Long Diagonal of Trapezoid Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Long = \sqrt{{15m}^{2} + {9m}^{2} - (2 \cdot 15m \cdot 9m \cdot \cos (70°))}

Next Step Convert Units

∴

d Long = \sqrt{{15m}^{2} + {9m}^{2} - (2 \cdot 15m \cdot 9m \cdot \cos (1.2217rad))}

Next Step Prepare to Evaluate

∴

d Long = \sqrt{15^{2} + 9^{2} - (2 \cdot 15 \cdot 9 \cdot \cos (1.2217))}

Next Step Evaluate

∴

d Long = 14.616927218195m

LAST Step Rounding Answer

∴

d Long = 14.6169m

Long Diagonal of Trapezoid 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

Long Base of Trapezoid

Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.

Symbol: B_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Base of Trapezoid

Short Leg of Trapezoid

Short Leg of Trapezoid is the shorter side among the pair of non parallel and opposite sides of the Trapezoid.

Symbol: L_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Leg of Trapezoid

Larger Acute Angle of Trapezoid

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

Symbol: ∠_{Larger Acute}

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Larger Acute 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 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 Short Diagonal

d Long = \frac{h \cdot (B Long + B Short)}{d Short \cdot \sin (∠ d(Leg))}

Other formulas in Long Diagonal of Trapezoid category

Go Short Diagonal of Trapezoid

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

Go Short Diagonal of Trapezoid given all Sides

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

Go Short Diagonal of Trapezoid given Long Diagonal

d Short = \frac{h \cdot (B Long + B Short)}{d Long \cdot \sin (∠ d(Leg))}

How to Evaluate Long Diagonal of Trapezoid?

Long Diagonal of Trapezoid evaluator uses 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))) to evaluate the Long Diagonal of Trapezoid, Long Diagonal of Trapezoid formula is defined as the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid. Long Diagonal of Trapezoid is denoted by d_Long symbol.

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

FAQs on Long Diagonal of Trapezoid

What is the formula to find Long Diagonal of Trapezoid?

The formula of Long Diagonal of Trapezoid is expressed as 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))). Here is an example- 14.61693 = sqrt(15^2+9^2-(2*15*9*cos(1.2217304763958))).

How to calculate Long Diagonal of Trapezoid?

With Long Base of Trapezoid (B_Long), Short Leg of Trapezoid (L_Short) & Larger Acute Angle of Trapezoid (∠_{Larger Acute}) we can find Long Diagonal of Trapezoid using the formula - 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))). 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(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=(Height of Trapezoid*(Long Base of Trapezoid+Short Base of Trapezoid))/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))

Can the Long Diagonal of Trapezoid be negative?

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

Which unit is used to measure Long Diagonal of Trapezoid?

Long Diagonal of Trapezoid 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 can be measured.

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Long Diagonal of Trapezoid Formula

​GoLong Diagonal of Trapezoid given all Sides Formula

​GoLong Diagonal of Trapezoid given Short Diagonal Formula

Long Diagonal of Trapezoid Example

Long Diagonal of Trapezoid Solution

Long Diagonal of Trapezoid Formula Elements

Other Formulas to find Long Diagonal of Trapezoid

Other formulas in Long Diagonal of Trapezoid category

How to Evaluate Long Diagonal of Trapezoid?

FAQs on Long Diagonal of Trapezoid

Variable Name

GoLong Diagonal of Trapezoid given all Sides Formula

GoLong Diagonal of Trapezoid given Short Diagonal Formula