Short Diagonal of Trapezoid given Long Leg 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%
✖Long Leg of Trapezoid is the longer side among the pair of non parallel and opposite sides of the Trapezoid.ⓘ Long Leg of Trapezoid [L_Long]			+10% -10%
✖Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.ⓘ Height of Trapezoid [h]			+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 given Long Leg [d_Short]

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Short Diagonal of Trapezoid given Long Leg Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Long Base of Trapezoid*sqrt(Long Leg of Trapezoid^2-Height of Trapezoid^2)))
d_Short = sqrt(B_Long^2+L_Long^2-(2*B_Long*sqrt(L_Long^2-h^2)))
This formula uses 1 Functions, 4 Variables

Functions Used

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

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.
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 Leg of Trapezoid - (Measured in Meter) - Long Leg of Trapezoid is the longer side among the pair of non parallel and opposite sides 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.

STEP 1: Convert Input(s) to Base Unit

Long Base of Trapezoid: 15 Meter --> 15 Meter No Conversion Required
Long Leg of Trapezoid: 11 Meter --> 11 Meter No Conversion Required
Height of Trapezoid: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Short = sqrt(B_Long^2+L_Long^2-(2*B_Long*sqrt(L_Long^2-h^2))) --> sqrt(15^2+11^2-(2*15*sqrt(11^2-8^2)))

Evaluating ... ...

d_Short = 10.9318327348106

STEP 3: Convert Result to Output's Unit

10.9318327348106 Meter --> No Conversion Required

FINAL ANSWER

10.9318327348106 ≈ 10.93183 Meter <-- Short Diagonal of Trapezoid

(Calculation completed in 00.004 seconds)

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< Short Diagonal of Trapezoid Calculators

Short Diagonal of Trapezoid given all Sides

LaTeX 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)))

Short Diagonal of Trapezoid given Short Leg

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

Short Diagonal of Trapezoid

LaTeX 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)))

Short Diagonal of Trapezoid given Height

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

Short Diagonal of Trapezoid given Long Leg Formula

LaTeX Go

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 Diagonal of Trapezoid given Long Leg?

Short Diagonal of Trapezoid given Long Leg calculator uses Short Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Long Base of Trapezoid*sqrt(Long Leg of Trapezoid^2-Height of Trapezoid^2))) to calculate the Short Diagonal of Trapezoid, Short Diagonal of Trapezoid given Long Leg formula is defined as the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid, and calculated using long leg of the Trapezoid. Short Diagonal of Trapezoid is denoted by d_Short symbol.

How to calculate Short Diagonal of Trapezoid given Long Leg using this online calculator? To use this online calculator for Short Diagonal of Trapezoid given Long Leg, enter Long Base of Trapezoid (B_Long), Long Leg of Trapezoid (L_Long) & Height of Trapezoid (h) and hit the calculate button. Here is how the Short Diagonal of Trapezoid given Long Leg calculation can be explained with given input values -> 10.93183 = sqrt(15^2+11^2-(2*15*sqrt(11^2-8^2))).

FAQ

What is Short Diagonal of Trapezoid given Long Leg?

Short Diagonal of Trapezoid given Long Leg formula is defined as the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid, and calculated using long leg of the Trapezoid and is represented as d_Short = sqrt(B_Long^2+L_Long^2-(2*B_Long*sqrt(L_Long^2-h^2))) or Short Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Long Base of Trapezoid*sqrt(Long Leg of Trapezoid^2-Height of Trapezoid^2))). Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid, Long Leg of Trapezoid is the longer side among the pair of non parallel and opposite sides of the Trapezoid & Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.

How to calculate Short Diagonal of Trapezoid given Long Leg?

Short Diagonal of Trapezoid given Long Leg formula is defined as the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid, and calculated using long leg of the Trapezoid is calculated using Short Diagonal of Trapezoid = sqrt(Long Base of Trapezoid^2+Long Leg of Trapezoid^2-(2*Long Base of Trapezoid*sqrt(Long Leg of Trapezoid^2-Height of Trapezoid^2))). To calculate Short Diagonal of Trapezoid given Long Leg, you need Long Base of Trapezoid (B_Long), Long Leg of Trapezoid (L_Long) & Height of Trapezoid (h). With our tool, you need to enter the respective value for Long Base of Trapezoid, Long Leg of Trapezoid & Height 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 Diagonal of Trapezoid?

In this formula, Short Diagonal of Trapezoid uses Long Base of Trapezoid, Long Leg of Trapezoid & Height of Trapezoid. We can use 3 other way(s) to calculate the same, which is/are as follows -

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

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