Long Diagonal of Trapezoid given Median and Short Diagonal Calculator

✖Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.ⓘ Height of Trapezoid [h]			+10% -10%
✖Central Median of Trapezoid is the length of the line joining the midpoints of both legs or the non parallel pair of opposite sides of the Trapezoid.ⓘ Central Median of Trapezoid [M]			+10% -10%
✖Short Diagonal of Trapezoid is the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid.ⓘ Short Diagonal of Trapezoid [d_Short]			+10% -10%
✖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.ⓘ Leg Angle between Diagonals of Trapezoid [∠_d(Leg)]			+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 given Median and Short Diagonal [d_Long]

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Long Diagonal of Trapezoid given Median and Short Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Diagonal of Trapezoid = (2*Height of Trapezoid*Central Median of Trapezoid)/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))
d_Long = (2*h*M)/(d_Short*sin(∠_d(Leg)))
This formula uses 1 Functions, 5 Variables

Functions Used

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., sin(Angle)

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.
Height of Trapezoid - (Measured in Meter) - Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.
Central Median of Trapezoid - (Measured in Meter) - Central Median of Trapezoid is the length of the line joining the midpoints of both legs or the non parallel pair of opposite sides of the Trapezoid.
Short Diagonal of Trapezoid - (Measured in Meter) - Short Diagonal of Trapezoid is the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid.
Leg Angle between Diagonals of Trapezoid - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Height of Trapezoid: 8 Meter --> 8 Meter No Conversion Required
Central Median of Trapezoid: 10 Meter --> 10 Meter No Conversion Required
Short Diagonal of Trapezoid: 12 Meter --> 12 Meter No Conversion Required
Leg Angle between Diagonals of Trapezoid: 80 Degree --> 1.3962634015952 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Long = (2*h*M)/(d_Short*sin(∠_d(Leg))) --> (2*8*10)/(12*sin(1.3962634015952))

Evaluating ... ...

d_Long = 13.5390214918106

STEP 3: Convert Result to Output's Unit

13.5390214918106 Meter --> No Conversion Required

FINAL ANSWER

13.5390214918106 ≈ 13.53902 Meter <-- Long Diagonal of Trapezoid

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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< Long Diagonal of Trapezoid Calculators

Long Diagonal of Trapezoid given all Sides

LaTeX 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

LaTeX 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

LaTeX 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 Height and Larger Acute Angle

LaTeX 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 Formula

LaTeX Go

Long Diagonal of Trapezoid = (2*Height of Trapezoid*Central Median of Trapezoid)/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))
d_Long = (2*h*M)/(d_Short*sin(∠_d(Leg)))

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 given Median and Short Diagonal?

Long Diagonal of Trapezoid given Median and Short Diagonal calculator uses Long Diagonal of Trapezoid = (2*Height of Trapezoid*Central Median of Trapezoid)/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid)) to calculate the Long Diagonal of Trapezoid, Long Diagonal of Trapezoid given Median and 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 height, central median and short diagonal of the Trapezoid. Long Diagonal of Trapezoid is denoted by d_Long symbol.

How to calculate Long Diagonal of Trapezoid given Median and Short Diagonal using this online calculator? To use this online calculator for Long Diagonal of Trapezoid given Median and Short Diagonal, enter Height of Trapezoid (h), Central Median of Trapezoid (M), Short Diagonal of Trapezoid (d_Short) & Leg Angle between Diagonals of Trapezoid (∠_d(Leg)) and hit the calculate button. Here is how the Long Diagonal of Trapezoid given Median and Short Diagonal calculation can be explained with given input values -> 13.53902 = (2*8*10)/(12*sin(1.3962634015952)).

FAQ

What is Long Diagonal of Trapezoid given Median and Short Diagonal?

Long Diagonal of Trapezoid given Median and 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 height, central median and short diagonal of the Trapezoid and is represented as d_Long = (2*h*M)/(d_Short*sin(∠_d(Leg))) or Long Diagonal of Trapezoid = (2*Height of Trapezoid*Central Median of Trapezoid)/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid)). Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid, Central Median of Trapezoid is the length of the line joining the midpoints of both legs or the non parallel pair of opposite sides of the 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 & 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.

How to calculate Long Diagonal of Trapezoid given Median and Short Diagonal?

Long Diagonal of Trapezoid given Median and 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 height, central median and short diagonal of the Trapezoid is calculated using Long Diagonal of Trapezoid = (2*Height of Trapezoid*Central Median of Trapezoid)/(Short Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid)). To calculate Long Diagonal of Trapezoid given Median and Short Diagonal, you need Height of Trapezoid (h), Central Median of Trapezoid (M), Short Diagonal of Trapezoid (d_Short) & Leg Angle between Diagonals of Trapezoid (∠_d(Leg)). With our tool, you need to enter the respective value for Height of Trapezoid, Central Median of Trapezoid, Short Diagonal of Trapezoid & Leg Angle between Diagonals 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 Height of Trapezoid, Central Median of Trapezoid, Short Diagonal of Trapezoid & Leg Angle between Diagonals of Trapezoid. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)))

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