Long 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%
✖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%
✖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%

✖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 Height [d_Long]

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Long Diagonal of Trapezoid given Height Solution

STEP 0: Pre-Calculation Summary

Formula Used

Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2)
d_Long = sqrt(h^2+(B_Short+(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

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.
Height of Trapezoid - (Measured in Meter) - Height of Trapezoid is the perpendicular distance between the pair of parallel sides 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.
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
Short Base of Trapezoid: 5 Meter --> 5 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_Long = sqrt(h^2+(B_Short+(h*cot(∠_{Smaller Acute})))^2) --> sqrt(8^2+(5+(8*cot(0.872664625997001)))^2)

Evaluating ... ...

d_Long = 14.1841324980033

STEP 3: Convert Result to Output's Unit

14.1841324980033 Meter --> No Conversion Required

FINAL ANSWER

14.1841324980033 ≈ 14.18413 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 Height Formula

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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 Height?

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

How to calculate Long Diagonal of Trapezoid given Height using this online calculator? To use this online calculator for Long Diagonal of Trapezoid given Height, enter Height of Trapezoid (h), Short Base of Trapezoid (B_Short) & Smaller Acute Angle of Trapezoid (∠_{Smaller Acute}) and hit the calculate button. Here is how the Long Diagonal of Trapezoid given Height calculation can be explained with given input values -> 14.18413 = sqrt(8^2+(5+(8*cot(0.872664625997001)))^2).

FAQ

What is Long Diagonal of Trapezoid given Height?

Long Diagonal of Trapezoid given Height 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 height of the Trapezoid and is represented as d_Long = sqrt(h^2+(B_Short+(h*cot(∠_{Smaller Acute})))^2) or Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short 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, Short Base of Trapezoid is the shorter 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 Long Diagonal of Trapezoid given Height?

Long Diagonal of Trapezoid given Height 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 height of the Trapezoid is calculated using Long Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Smaller Acute Angle of Trapezoid)))^2). To calculate Long Diagonal of Trapezoid given Height, you need Height of Trapezoid (h), Short Base of Trapezoid (B_Short) & Smaller Acute Angle of Trapezoid (∠_{Smaller Acute}). With our tool, you need to enter the respective value for Height of Trapezoid, Short 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 Long Diagonal of Trapezoid?

In this formula, Long Diagonal of Trapezoid uses Height of Trapezoid, Short Base of Trapezoid & Smaller Acute Angle 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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