Short Diagonal of Trapezoid given Height Calculator

✖Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.ⓘ Height of Trapezoid [h]			+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%
✖Smaller Acute Angle of Trapezoid is the smaller angle on the long base or the angle made by the long base and long leg of the Trapezoid.ⓘ Smaller Acute Angle of Trapezoid [∠_{Smaller Acute}]			+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 Height [d_Short]

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Formula

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Short Diagonal of Trapezoid given Height

Formula

`"d"_{"Short"} = sqrt("h"^2+("B"_{"Long"}-("h"*cot("∠"_{"Smaller Acute"})))^2)`

Example

`"11.51858m"=sqrt(("8m")^2+("15m"-("8m"*cot("50°")))^2)`

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Short Diagonal of Trapezoid given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2)
d_Short = sqrt(h^2+(B_Long-(h*cot(∠_{Smaller Acute})))^2)
This formula uses 2 Functions, 4 Variables

Functions Used

cot - Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle., cot(Angle)
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.
Height of Trapezoid - (Measured in Meter) - Height of Trapezoid is the perpendicular distance between the pair of parallel sides 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.
Smaller Acute Angle of Trapezoid - (Measured in Radian) - Smaller Acute Angle of Trapezoid is the smaller angle on the long base or the angle made by the long base and long leg of the Trapezoid.

STEP 1: Convert Input(s) to Base Unit

Height of Trapezoid: 8 Meter --> 8 Meter No Conversion Required
Long Base of Trapezoid: 15 Meter --> 15 Meter No Conversion Required
Smaller Acute Angle of Trapezoid: 50 Degree --> 0.872664625997001 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d_Short = sqrt(h^2+(B_Long-(h*cot(∠_{Smaller Acute})))^2) --> sqrt(8^2+(15-(8*cot(0.872664625997001)))^2)

Evaluating ... ...

d_Short = 11.5185820630881

STEP 3: Convert Result to Output's Unit

11.5185820630881 Meter --> No Conversion Required

FINAL ANSWER

11.5185820630881 ≈ 11.51858 Meter <-- Short Diagonal of Trapezoid

(Calculation completed in 00.004 seconds)

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< 10+ Short Diagonal of Trapezoid Calculators

Short Diagonal of Trapezoid given all Sides

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

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

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 Long Leg

Go 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)))

Short Diagonal of Trapezoid given Long Diagonal

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

Short Diagonal of Trapezoid given Long Diagonal and all Sides

Go Short Diagonal of Trapezoid = sqrt(Long Leg of Trapezoid^2+Short Leg of Trapezoid^2+(2*Long Base of Trapezoid*Short Base of Trapezoid)-Long Diagonal of Trapezoid^2)

Short Diagonal of Trapezoid given Height and Larger Acute Angle

Go Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2)

Short Diagonal of Trapezoid given Height

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 Median and Long Diagonal

Go Short Diagonal of Trapezoid = (2*Height of Trapezoid*Central Median of Trapezoid)/(Long Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))

Short Diagonal of Trapezoid given Area and Long Diagonal

Go Short Diagonal of Trapezoid = (2*Area of Trapezoid)/(Long Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))

Short Diagonal of Trapezoid given Height 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 Diagonal of Trapezoid given Height?

Short Diagonal of Trapezoid given Height calculator uses Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2) to calculate the Short Diagonal of Trapezoid, Short Diagonal of Trapezoid given Height 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 height of the Trapezoid. Short Diagonal of Trapezoid is denoted by d_Short symbol.

How to calculate Short Diagonal of Trapezoid given Height using this online calculator? To use this online calculator for Short Diagonal of Trapezoid given Height, enter Height of Trapezoid (h), Long Base of Trapezoid (B_Long) & Smaller Acute Angle of Trapezoid (∠_{Smaller Acute}) and hit the calculate button. Here is how the Short Diagonal of Trapezoid given Height calculation can be explained with given input values -> 11.51858 = sqrt(8^2+(15-(8*cot(0.872664625997001)))^2).

FAQ

What is Short Diagonal of Trapezoid given Height?

Short Diagonal of Trapezoid given Height 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 height of the Trapezoid and is represented as d_Short = sqrt(h^2+(B_Long-(h*cot(∠_{Smaller Acute})))^2) or Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2). Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid, Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid & Smaller Acute Angle of Trapezoid is the smaller angle on the long base or the angle made by the long base and long leg of the Trapezoid.

How to calculate Short Diagonal of Trapezoid given Height?

Short Diagonal of Trapezoid given Height 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 height of the Trapezoid is calculated using Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Long Base of Trapezoid-(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2). To calculate Short Diagonal of Trapezoid given Height, you need Height of Trapezoid (h), Long Base of Trapezoid (B_Long) & Smaller Acute Angle of Trapezoid (∠_{Smaller Acute}). With our tool, you need to enter the respective value for Height of Trapezoid, Long Base of Trapezoid & Smaller Acute Angle 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 Height of Trapezoid, Long Base of Trapezoid & Smaller Acute Angle of Trapezoid. We can use 9 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)))
Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2)
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)))
Short Diagonal of Trapezoid = (Height of Trapezoid*(Long Base of Trapezoid+Short Base of Trapezoid))/(Long Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))
Short Diagonal of Trapezoid = (2*Height of Trapezoid*Central Median of Trapezoid)/(Long Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))
Short Diagonal of Trapezoid = (2*Area of Trapezoid)/(Long Diagonal of Trapezoid*sin(Leg Angle between Diagonals of Trapezoid))
Short Diagonal of Trapezoid = sqrt(Long Leg of Trapezoid^2+Short Leg of Trapezoid^2+(2*Long Base of Trapezoid*Short Base of Trapezoid)-Long Diagonal of Trapezoid^2)

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