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Long Diagonal of Trapezoid given Short Leg 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{{B Long}^{2} + {L Short}^{2} - (2 \cdot B Long \cdot \sqrt{{L Short}^{2} - h^{2}})}

d_Long - Long Diagonal of Trapezoid?B_Long - Long Base of Trapezoid?L_Short - Short Leg of Trapezoid?h - Height of Trapezoid?

Long Diagonal of Trapezoid given Short Leg Example

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

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

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

13.5021 = \sqrt{15^{2} + 9^{2} - (2 \cdot 15 \cdot \sqrt{9^{2} - 8^{2}})}

13.5021m = \sqrt{{15m}^{2} + {9m}^{2} - (2 \cdot 15m \cdot \sqrt{{9m}^{2} - {8m}^{2}})}

13.5021 = \sqrt{15^{2} + 9^{2} - (2 \cdot 15 \cdot \sqrt{9^{2} - 8^{2}})}

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Long Diagonal of Trapezoid given Short Leg Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Long = \sqrt{{15m}^{2} + {9m}^{2} - (2 \cdot 15m \cdot \sqrt{{9m}^{2} - {8m}^{2}})}

Next Step Prepare to Evaluate

∴

d Long = \sqrt{15^{2} + 9^{2} - (2 \cdot 15 \cdot \sqrt{9^{2} - 8^{2}})}

Next Step Evaluate

∴

d Long = 13.5021046963601m

LAST Step Rounding Answer

∴

d Long = 13.5021m

Long Diagonal of Trapezoid given Short 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

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

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

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 Short Leg?

Long Diagonal of Trapezoid given Short Leg evaluator uses Long Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Short Leg of Trapezoid^2-(2*Long Base of Trapezoid*sqrt(Short Leg of Trapezoid^2-Height of Trapezoid^2))) to evaluate the Long Diagonal of Trapezoid, Long Diagonal of Trapezoid given Short 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 short leg of the Trapezoid. Long Diagonal of Trapezoid is denoted by d_Long symbol.

How to evaluate Long Diagonal of Trapezoid given Short Leg using this online evaluator? To use this online evaluator for Long Diagonal of Trapezoid given Short Leg, enter Long Base of Trapezoid (B_Long), Short Leg of Trapezoid (L_Short) & Height of Trapezoid (h) and hit the calculate button.

FAQs on Long Diagonal of Trapezoid given Short Leg

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

The formula of Long Diagonal of Trapezoid given Short Leg is expressed as Long Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Short Leg of Trapezoid^2-(2*Long Base of Trapezoid*sqrt(Short Leg of Trapezoid^2-Height of Trapezoid^2))). Here is an example- 13.5021 = sqrt(15^2+9^2-(2*15*sqrt(9^2-8^2))).

How to calculate Long Diagonal of Trapezoid given Short Leg?

With Long Base of Trapezoid (B_Long), Short Leg of Trapezoid (L_Short) & Height of Trapezoid (h) we can find Long Diagonal of Trapezoid given Short Leg using the formula - Long Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Short Leg of Trapezoid^2-(2*Long Base of Trapezoid*sqrt(Short Leg of Trapezoid^2-Height of Trapezoid^2))). This formula also uses 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 Short Leg be negative?

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

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

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

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Long Diagonal of Trapezoid given Short Leg Formula

​GoLong Diagonal of Trapezoid Formula

​GoLong Diagonal of Trapezoid given Long Leg Formula

Long Diagonal of Trapezoid given Short Leg Example

Long Diagonal of Trapezoid given Short Leg Solution

Long Diagonal of Trapezoid given Short Leg Formula Elements

Other Formulas to find Long Diagonal of Trapezoid

How to Evaluate Long Diagonal of Trapezoid given Short Leg?

FAQs on Long Diagonal of Trapezoid given Short Leg

Variable Name

GoLong Diagonal of Trapezoid Formula

GoLong Diagonal of Trapezoid given Long Leg Formula