Long Diagonal of Trapezoid given Short 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%
✖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%
✖Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.ⓘ Height of Trapezoid [h]			+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 Short Leg [d_Long]

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Long Diagonal of Trapezoid given Short Leg 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*sqrt(Short Leg of Trapezoid^2-Height of Trapezoid^2)))
d_Long = sqrt(B_Long^2+L_Short^2-(2*B_Long*sqrt(L_Short^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

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.
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
Short Leg of Trapezoid: 9 Meter --> 9 Meter No Conversion Required
Height of Trapezoid: 8 Meter --> 8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Long = sqrt(B_Long^2+L_Short^2-(2*B_Long*sqrt(L_Short^2-h^2))) --> sqrt(15^2+9^2-(2*15*sqrt(9^2-8^2)))

Evaluating ... ...

d_Long = 13.5021046963601

STEP 3: Convert Result to Output's Unit

13.5021046963601 Meter --> No Conversion Required

FINAL ANSWER

13.5021046963601 ≈ 13.5021 Meter <-- Long Diagonal of Trapezoid

(Calculation completed in 00.004 seconds)

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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 Short 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 Long Diagonal of Trapezoid given Short Leg?

Long Diagonal of Trapezoid given Short Leg calculator uses 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))) to calculate the Long Diagonal of Trapezoid, Long Diagonal of Trapezoid given Short Leg 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 short leg of the Trapezoid. Long Diagonal of Trapezoid is denoted by d_Long symbol.

How to calculate Long Diagonal of Trapezoid given Short Leg using this online calculator? To use this online calculator for Long Diagonal of Trapezoid given Short Leg, enter Long Base of Trapezoid (B_Long), Short Leg of Trapezoid (L_Short) & Height of Trapezoid (h) and hit the calculate button. Here is how the Long Diagonal of Trapezoid given Short Leg calculation can be explained with given input values -> 13.5021 = sqrt(15^2+9^2-(2*15*sqrt(9^2-8^2))).

FAQ

What is Long Diagonal of Trapezoid given Short Leg?

Long Diagonal of Trapezoid given Short Leg 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 short leg of the Trapezoid and is represented as d_Long = sqrt(B_Long^2+L_Short^2-(2*B_Long*sqrt(L_Short^2-h^2))) or 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 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 & Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.

How to calculate Long Diagonal of Trapezoid given Short Leg?

Long Diagonal of Trapezoid given Short Leg 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 short leg 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*sqrt(Short Leg of Trapezoid^2-Height of Trapezoid^2))). To calculate Long Diagonal of Trapezoid given Short Leg, you need Long Base of Trapezoid (B_Long), Short Leg of Trapezoid (L_Short) & Height of Trapezoid (h). With our tool, you need to enter the respective value for Long Base of Trapezoid, Short 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 Long Diagonal of Trapezoid?

In this formula, Long Diagonal of Trapezoid uses Long Base of Trapezoid, Short Leg of Trapezoid & Height 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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