Short 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%
✖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 Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid.ⓘ Short Base of Trapezoid given Height and Both Diagonals [B_Short]

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Formula

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Short Base of Trapezoid given Height and Both Diagonals

Formula

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

Example

`"5.680963m"=(("14m"*"12m")/"8m"*sin("80°"))-"15m"`

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Short Base of Trapezoid given Height and Both Diagonals Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

Short Base of Trapezoid - (Measured in Meter) - Short Base of Trapezoid is the shorter 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.
Long Base of Trapezoid - (Measured in Meter) - Long Base of Trapezoid is the longer 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)
Long Base of Trapezoid: 15 Meter --> 15 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

B_Short = ((d_Long*d_Short)/h*sin(∠_d(Leg)))-B_Long --> ((14*12)/8*sin(1.3962634015952))-15

Evaluating ... ...

B_Short = 5.68096281325541

STEP 3: Convert Result to Output's Unit

5.68096281325541 Meter --> No Conversion Required

FINAL ANSWER

5.68096281325541 ≈ 5.680963 Meter <-- Short Base of Trapezoid

(Calculation completed in 00.020 seconds)

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Home » Math » Geometry » 2D Geometry » Trapezoid » Sides of Trapezoid » Short Base of Trapezoid » Short 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 Short Base of Trapezoid Calculators

Short Base of Trapezoid given Short Leg

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

Short Base of Trapezoid given Long Leg

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

Short Base of Trapezoid given Height and Both Diagonals

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

Short Base of Trapezoid given Height

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

Short Base of Trapezoid

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

Short Base of Trapezoid given Central Median

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

Short 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 Short Base of Trapezoid given Height and Both Diagonals?

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

How to calculate Short Base of Trapezoid given Height and Both Diagonals using this online calculator? To use this online calculator for Short 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)) & Long Base of Trapezoid (B_Long) and hit the calculate button. Here is how the Short Base of Trapezoid given Height and Both Diagonals calculation can be explained with given input values -> 5.680963 = ((14*12)/8*sin(1.3962634015952))-15.

FAQ

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

Short Base of Trapezoid given Height and Both Diagonals formula is defined as the shorter 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_Short = ((d_Long*d_Short)/h*sin(∠_d(Leg)))-B_Long or Short Base of Trapezoid = ((Long Diagonal of Trapezoid*Short Diagonal of Trapezoid)/Height of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))-Long 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 & Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.

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

Short Base of Trapezoid given Height and Both Diagonals formula is defined as the shorter side among the pair of parallel sides of the Trapezoid, and calculated using the height and both diagonals of the Trapezoid is calculated using Short Base of Trapezoid = ((Long Diagonal of Trapezoid*Short Diagonal of Trapezoid)/Height of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))-Long Base of Trapezoid. To calculate Short 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)) & Long Base of Trapezoid (B_Long). 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 & Long 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 Short Base of Trapezoid?

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

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

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