Long Base of Trapezoid given Height and Both Diagonals Calculator

✖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]			+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%
✖Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.ⓘ Height of Trapezoid [h]			+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%
✖Short Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid.ⓘ Short Base of Trapezoid [B_Short]			+10% -10%

✖Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.ⓘ Long Base of Trapezoid given Height and Both Diagonals [B_Long]

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Formula

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Long Base of Trapezoid given Height and Both Diagonals

Formula

`"B"_{"Long"} = (("d"_{"Long"}*"d"_{"Short"})/"h"*sin("∠"_{"d(Leg)"}))-"B"_{"Short"}`

Example

`"15.68096m"=(("14m"*"12m")/"8m"*sin("80°"))-"5m"`

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Long Base of Trapezoid given Height and Both Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Base of Trapezoid = ((Long Diagonal of Trapezoid*Short Diagonal of Trapezoid)/Height of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))-Short Base of Trapezoid
B_Long = ((d_Long*d_Short)/h*sin(∠_d(Leg)))-B_Short
This formula uses 1 Functions, 6 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 Base of Trapezoid - (Measured in Meter) - Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.
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.
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.
Height of Trapezoid - (Measured in Meter) - Height of Trapezoid is the perpendicular distance between the pair of parallel sides 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.
Short Base of Trapezoid - (Measured in Meter) - Short Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid.

STEP 1: Convert Input(s) to Base Unit

Long Diagonal of Trapezoid: 14 Meter --> 14 Meter No Conversion Required
Short Diagonal of Trapezoid: 12 Meter --> 12 Meter No Conversion Required
Height of Trapezoid: 8 Meter --> 8 Meter No Conversion Required
Leg Angle between Diagonals of Trapezoid: 80 Degree --> 1.3962634015952 Radian (Check conversion here)
Short Base of Trapezoid: 5 Meter --> 5 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

B_Long = ((d_Long*d_Short)/h*sin(∠_d(Leg)))-B_Short --> ((14*12)/8*sin(1.3962634015952))-5

Evaluating ... ...

B_Long = 15.6809628132554

STEP 3: Convert Result to Output's Unit

15.6809628132554 Meter --> No Conversion Required

FINAL ANSWER

15.6809628132554 ≈ 15.68096 Meter <-- Long Base of Trapezoid

(Calculation completed in 00.004 seconds)

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Home » Math » Geometry » 2D Geometry » Trapezoid » Sides of Trapezoid » Long Base of Trapezoid » Long Base of Trapezoid given Height and Both Diagonals

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Indian Institute of Technology (IIT), Mumbai

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< 6 Long Base of Trapezoid Calculators

Long Base of Trapezoid given Short Leg

Go Long Base of Trapezoid = Short Base of Trapezoid+(Short Leg of Trapezoid*(sin(Smaller Acute Angle of Trapezoid+Larger Acute Angle of Trapezoid))/(sin(Smaller Acute Angle of Trapezoid)))

Long Base of Trapezoid given Long Leg

Go Long Base of Trapezoid = Short Base of Trapezoid+(Long Leg of Trapezoid*(sin(Smaller Acute Angle of Trapezoid+Larger Acute Angle of Trapezoid))/(sin(Larger Acute Angle of Trapezoid)))

Long Base of Trapezoid given Height and Both Diagonals

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

Long Base of Trapezoid given Height

Go Long Base of Trapezoid = Short Base of Trapezoid+(Height of Trapezoid*(cot(Larger Acute Angle of Trapezoid)+cot(Smaller Acute Angle of Trapezoid)))

Long Base of Trapezoid

Go Long Base of Trapezoid = (2*Area of Trapezoid)/Height of Trapezoid-Short Base of Trapezoid

Long Base of Trapezoid given Central Median

Go Long Base of Trapezoid = (2*Central Median of Trapezoid)-Short Base of Trapezoid

Long Base of Trapezoid given Height and Both Diagonals 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 Base of Trapezoid given Height and Both Diagonals?

Long Base of Trapezoid given Height and Both Diagonals calculator uses Long Base of Trapezoid = ((Long Diagonal of Trapezoid*Short Diagonal of Trapezoid)/Height of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))-Short Base of Trapezoid to calculate the Long Base of Trapezoid, Long Base of Trapezoid given Height and Both Diagonals formula is defined as the longer side among the pair of parallel sides of the Trapezoid, and calculated using the height and both diagonals of the Trapezoid. Long Base of Trapezoid is denoted by B_Long symbol.

How to calculate Long Base of Trapezoid given Height and Both Diagonals using this online calculator? To use this online calculator for Long Base of Trapezoid given Height and Both Diagonals, enter Long Diagonal of Trapezoid (d_Long), Short Diagonal of Trapezoid (d_Short), Height of Trapezoid (h), Leg Angle between Diagonals of Trapezoid (∠_d(Leg)) & Short Base of Trapezoid (B_Short) and hit the calculate button. Here is how the Long Base of Trapezoid given Height and Both Diagonals calculation can be explained with given input values -> 15.68096 = ((14*12)/8*sin(1.3962634015952))-5.

FAQ

What is Long Base of Trapezoid given Height and Both Diagonals?

Long Base of Trapezoid given Height and Both Diagonals formula is defined as the longer side among the pair of parallel sides of the Trapezoid, and calculated using the height and both diagonals of the Trapezoid and is represented as B_Long = ((d_Long*d_Short)/h*sin(∠_d(Leg)))-B_Short or Long Base of Trapezoid = ((Long Diagonal of Trapezoid*Short Diagonal of Trapezoid)/Height of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))-Short Base 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, Short Diagonal of Trapezoid is the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid, Height of Trapezoid is the perpendicular distance between the pair of parallel sides 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 & Short Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid.

How to calculate Long Base of Trapezoid given Height and Both Diagonals?

Long Base of Trapezoid given Height and Both Diagonals formula is defined as the longer side among the pair of parallel sides of the Trapezoid, and calculated using the height and both diagonals of the Trapezoid is calculated using Long Base of Trapezoid = ((Long Diagonal of Trapezoid*Short Diagonal of Trapezoid)/Height of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))-Short Base of Trapezoid. To calculate Long Base of Trapezoid given Height and Both Diagonals, you need Long Diagonal of Trapezoid (d_Long), Short Diagonal of Trapezoid (d_Short), Height of Trapezoid (h), Leg Angle between Diagonals of Trapezoid (∠_d(Leg)) & Short Base of Trapezoid (B_Short). With our tool, you need to enter the respective value for Long Diagonal of Trapezoid, Short Diagonal of Trapezoid, Height of Trapezoid, Leg Angle between Diagonals of Trapezoid & Short Base 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 Base of Trapezoid?

In this formula, Long Base of Trapezoid uses Long Diagonal of Trapezoid, Short Diagonal of Trapezoid, Height of Trapezoid, Leg Angle between Diagonals of Trapezoid & Short Base of Trapezoid. We can use 5 other way(s) to calculate the same, which is/are as follows -

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

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