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Long Diagonal of Trapezoid given Short Diagonal Formula

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

d_Long - Long Diagonal of Trapezoid?h - Height of Trapezoid?B_Long - Long Base of Trapezoid?B_Short - Short Base of Trapezoid?d_Short - Short Diagonal of Trapezoid?∠_d(Leg) - Leg Angle between Diagonals of Trapezoid?

Long Diagonal of Trapezoid given Short Diagonal Example

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

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

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

13.539 = \frac{8 \cdot (15 + 5)}{12 \cdot \sin (80)}

13.539m = \frac{8m \cdot (15m + 5m)}{12m \cdot \sin (80°)}

13.539 = \frac{8 \cdot (15 + 5)}{12 \cdot \sin (80)}

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Long Diagonal of Trapezoid given Short Diagonal Solution

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

FIRST Step Consider the formula

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

Next Step Substitute values of Variables

∴

d Long = \frac{8m \cdot (15m + 5m)}{12m \cdot \sin (80°)}

Next Step Convert Units

∴

d Long = \frac{8m \cdot (15m + 5m)}{12m \cdot \sin (1.3963rad)}

Next Step Prepare to Evaluate

∴

d Long = \frac{8 \cdot (15 + 5)}{12 \cdot \sin (1.3963)}

Next Step Evaluate

∴

d Long = 13.5390214918106m

LAST Step Rounding Answer

∴

d Long = 13.539m

Long Diagonal of Trapezoid given Short Diagonal 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

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 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

Short Diagonal of Trapezoid

Short Diagonal of Trapezoid is the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid.

Symbol: d_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Diagonal of Trapezoid

Leg Angle between Diagonals of Trapezoid

Leg Angle between Diagonals of Trapezoid is the angle made by the diagonals of the Trapezoid which is near to any of the pair of non parallel and opposite legs of the Trapezoid.

Symbol: ∠_d(Leg)

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Leg Angle between Diagonals of Trapezoid

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

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})}

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 given Short Diagonal?

Long Diagonal of Trapezoid given Short Diagonal evaluator uses 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)) to evaluate the Long Diagonal of Trapezoid, Long Diagonal of Trapezoid given Short Diagonal 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 diagonal of the Trapezoid. Long Diagonal of Trapezoid is denoted by d_Long symbol.

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

FAQs on Long Diagonal of Trapezoid given Short Diagonal

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

The formula of Long Diagonal of Trapezoid given Short Diagonal is expressed as 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)). Here is an example- 13.53902 = (8*(15+5))/(12*sin(1.3962634015952)).

How to calculate Long Diagonal of Trapezoid given Short Diagonal?

With Height of Trapezoid (h), Long Base of Trapezoid (B_Long), Short Base of Trapezoid (B_Short), Short Diagonal of Trapezoid (d_Short) & Leg Angle between Diagonals of Trapezoid (∠_d(Leg)) we can find Long Diagonal of Trapezoid given Short Diagonal using the formula - 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)). This formula also uses Sine (sin) 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)))

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

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

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

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

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Long Diagonal of Trapezoid given Short Diagonal Formula

​GoLong Diagonal of Trapezoid Formula

​GoLong Diagonal of Trapezoid given all Sides Formula

Long Diagonal of Trapezoid given Short Diagonal Example

Long Diagonal of Trapezoid given Short Diagonal Solution

Long Diagonal of Trapezoid given Short Diagonal 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 given Short Diagonal?

FAQs on Long Diagonal of Trapezoid given Short Diagonal

Variable Name

GoLong Diagonal of Trapezoid Formula

GoLong Diagonal of Trapezoid given all Sides Formula