Long Diagonal of Trapezoid Calculator

✖Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.ⓘ Long Base of Trapezoid [B_Long]			+10% -10%
✖Short Leg of Trapezoid is the shorter side among the pair of non parallel and opposite sides of the Trapezoid.ⓘ Short Leg of Trapezoid [L_Short]			+10% -10%
✖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.ⓘ Larger Acute Angle of Trapezoid [∠_{Larger Acute}]			+10% -10%

✖Long Diagonal of Trapezoid is the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid.ⓘ Long Diagonal of Trapezoid [d_Long]

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Formula

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Long Diagonal of Trapezoid

Formula

`"d"_{"Long"} = sqrt("B"_{"Long"}^2+"L"_{"Short"}^2-(2*"B"_{"Long"}*"L"_{"Short"}*cos("∠"_{"Larger Acute"})))`

Example

`"14.61693m"=sqrt(("15m")^2+("9m")^2-(2*"15m"*"9m"*cos("70°")))`

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Long Diagonal of Trapezoid Solution

STEP 0: Pre-Calculation Summary

Formula Used

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)))
d_Long = sqrt(B_Long^2+L_Short^2-(2*B_Long*L_Short*cos(∠_{Larger Acute})))
This formula uses 2 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., 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., sqrt(Number)

Variables Used

Long Diagonal of Trapezoid - (Measured in Meter) - Long Diagonal of Trapezoid is the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid.
Long Base of Trapezoid - (Measured in Meter) - Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.
Short Leg of Trapezoid - (Measured in Meter) - Short Leg of Trapezoid is the shorter side among the pair of non parallel and opposite sides of the Trapezoid.
Larger Acute Angle of Trapezoid - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Long Base of Trapezoid: 15 Meter --> 15 Meter No Conversion Required
Short Leg of Trapezoid: 9 Meter --> 9 Meter No Conversion Required
Larger Acute Angle of Trapezoid: 70 Degree --> 1.2217304763958 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Long = sqrt(B_Long^2+L_Short^2-(2*B_Long*L_Short*cos(∠_{Larger Acute}))) --> sqrt(15^2+9^2-(2*15*9*cos(1.2217304763958)))

Evaluating ... ...

d_Long = 14.616927218195

STEP 3: Convert Result to Output's Unit

14.616927218195 Meter --> No Conversion Required

FINAL ANSWER

14.616927218195 ≈ 14.61693 Meter <-- Long Diagonal of Trapezoid

(Calculation completed in 00.020 seconds)

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< 10+ Long Diagonal of Trapezoid Calculators

Long Diagonal of Trapezoid given all Sides

Go 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 given Long Leg

Go 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

Go 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 given Short Leg

Go 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)))

Long Diagonal of Trapezoid given Short Diagonal

Go 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))

Long Diagonal of Trapezoid given Short Diagonal and all Sides

Go Long Diagonal of Trapezoid = sqrt(Long Leg of Trapezoid^2+Short Leg of Trapezoid^2+(2*Long Base of Trapezoid*Short Base of Trapezoid)-Short Diagonal of Trapezoid^2)

Long Diagonal of Trapezoid given Height

Go Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2)

Long Diagonal of Trapezoid given Height and Larger Acute Angle

Go Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2)

Long Diagonal of Trapezoid given Median and Short Diagonal

Go Long Diagonal of Trapezoid = (2*Height of Trapezoid*Central Median of Trapezoid)/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))

Long Diagonal of Trapezoid given Area and Short Diagonal

Go Long Diagonal of Trapezoid = (2*Area of Trapezoid)/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))

< 6 Diagonal of Trapezoid Calculators

Short Diagonal of Trapezoid given all Sides

Go Short Diagonal of Trapezoid = sqrt(Long Leg of Trapezoid^2+(Short Base of Trapezoid*Long Base of Trapezoid)-(Long Base of Trapezoid*(Long Leg of Trapezoid^2-Short Leg of Trapezoid^2)/(Long Base of Trapezoid-Short Base of Trapezoid)))

Long Diagonal of Trapezoid given all Sides

Short Diagonal of Trapezoid

Go Short Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Long Base of Trapezoid*Long Leg of Trapezoid*cos(Smaller Acute Angle of Trapezoid)))

Long Diagonal of Trapezoid

Go 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 given Short Diagonal

Go 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))

Short Diagonal of Trapezoid given Long Diagonal

Go Short Diagonal of Trapezoid = (Height of Trapezoid*(Long Base of Trapezoid+Short Base of Trapezoid))/(Long Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))

Long Diagonal of Trapezoid Formula

What is a Trapezoid?

Trapezoid is a quadrilateral with one pair of opposite and parallel sides. The pair of parallel sides is called the bases of the Trapezoid and the pair of non parallel edges is called the legs of the Trapezoid. Out of the four angles, in general a Trapezoid has 2 acute angles and 2 obtuse angles which are pairwise supplementary angles.

How to Calculate Long Diagonal of Trapezoid?

Long Diagonal of Trapezoid calculator 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 calculate 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 calculate Long Diagonal of Trapezoid using this online calculator? To use this online calculator 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. Here is how the Long Diagonal of Trapezoid calculation can be explained with given input values -> 14.61693 = sqrt(15^2+9^2-(2*15*9*cos(1.2217304763958))).

FAQ

What is 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 and is represented as d_Long = sqrt(B_Long^2+L_Short^2-(2*B_Long*L_Short*cos(∠_{Larger Acute}))) or 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 Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid, Short Leg of Trapezoid is the shorter side among the pair of non parallel and opposite sides of the 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.

How to calculate 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 is calculated using 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 calculate Long Diagonal of Trapezoid, you need Long Base of Trapezoid (B_Long), Short Leg of Trapezoid (L_Short) & Larger Acute Angle of Trapezoid (∠_{Larger Acute}). With our tool, you need to enter the respective value for Long Base of Trapezoid, Short Leg of Trapezoid & Larger Acute Angle of Trapezoid and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Long Diagonal of Trapezoid?

In this formula, Long Diagonal of Trapezoid uses Long Base of Trapezoid, Short Leg of Trapezoid & Larger Acute Angle of Trapezoid. We can use 11 other way(s) to calculate the same, which is/are as follows -

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)))
Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2)
Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2)
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)))
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))
Long Diagonal of Trapezoid = (2*Height of Trapezoid*Central Median of Trapezoid)/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))
Long Diagonal of Trapezoid = (2*Area of Trapezoid)/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))
Long Diagonal of Trapezoid = sqrt(Long Leg of Trapezoid^2+Short Leg of Trapezoid^2+(2*Long Base of Trapezoid*Short Base of Trapezoid)-Short Diagonal of Trapezoid^2)
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))

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