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Short Diagonal of Trapezoid given Height and Larger Acute Angle Formula

GoShort Diagonal of Trapezoid Formula

GoShort Diagonal of Trapezoid given Short Leg Formula

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Short Diagonal of Trapezoid is the length of the line joining the corners of larger acute angle and larger obtuse angle of the Trapezoid. Check FAQs

d Short = \sqrt{h^{2} + {(B Short + (h \cdot \cot (∠ Larger Acute)))}^{2}}

d_Short - Short Diagonal of Trapezoid?h - Height of Trapezoid?B_Short - Short Base of Trapezoid?∠_{Larger Acute} - Larger Acute Angle of Trapezoid?

Short Diagonal of Trapezoid given Height and Larger Acute Angle Example

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Here is how the Short Diagonal of Trapezoid given Height and Larger Acute Angle equation looks like with Values.

Here is how the Short Diagonal of Trapezoid given Height and Larger Acute Angle equation looks like with Units.

Here is how the Short Diagonal of Trapezoid given Height and Larger Acute Angle equation looks like.

11.2515 = \sqrt{8^{2} + {(5 + (8 \cdot \cot (70)))}^{2}}

11.2515m = \sqrt{{8m}^{2} + {(5m + (8m \cdot \cot (70°)))}^{2}}

11.2515 = \sqrt{8^{2} + {(5 + (8 \cdot \cot (70)))}^{2}}

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Short Diagonal of Trapezoid given Height and Larger Acute Angle Solution

Follow our step by step solution on how to calculate Short Diagonal of Trapezoid given Height and Larger Acute Angle?

FIRST Step Consider the formula

d Short = \sqrt{h^{2} + {(B Short + (h \cdot \cot (∠ Larger Acute)))}^{2}}

Next Step Substitute values of Variables

∴

d Short = \sqrt{{8m}^{2} + {(5m + (8m \cdot \cot (70°)))}^{2}}

Next Step Convert Units

∴

d Short = \sqrt{{8m}^{2} + {(5m + (8m \cdot \cot (1.2217rad)))}^{2}}

Next Step Prepare to Evaluate

∴

d Short = \sqrt{8^{2} + {(5 + (8 \cdot \cot (1.2217)))}^{2}}

Next Step Evaluate

∴

d Short = 11.2514877217621m

LAST Step Rounding Answer

∴

d Short = 11.2515m

Short Diagonal of Trapezoid given Height and Larger Acute Angle Formula Elements

Variables

Functions

Short Diagonal of 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.

Symbol: d_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Diagonal of Trapezoid

Height of Trapezoid

Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Trapezoid

Short Base of Trapezoid

Short Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid.

Symbol: B_Short

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Short Base of Trapezoid

Larger Acute Angle of Trapezoid

Larger Acute Angle of Trapezoid is the larger angle on the long base or the angle made by the long base and short leg of the Trapezoid.

Symbol: ∠_{Larger Acute}

Measurement: AngleUnit: °

Note: Value should be between 0 to 90.

Formulas to find Larger Acute Angle of Trapezoid

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: 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.

Syntax: sqrt(Number)

Other Formulas to find Short Diagonal of Trapezoid

Go Short Diagonal of Trapezoid

d Short = \sqrt{{B Long}^{2} + {L Long}^{2} - (2 \cdot B Long \cdot L Long \cdot \cos (∠ Smaller Acute))}

Go Short Diagonal of Trapezoid given Short Leg

d Short = \sqrt{{B Short}^{2} + {L Short}^{2} - (2 \cdot B Short \cdot L Short \cdot \cos (∠ Smaller Obtuse))}

Go Short Diagonal of Trapezoid given all Sides

d Short = \sqrt{{L Long}^{2} + (B Short \cdot B Long) - (B Long \cdot \frac{{L Long}^{2} - {L Short}^{2}}{B Long - B Short})}

Go Short Diagonal of Trapezoid given Height

d Short = \sqrt{h^{2} + {(B Long - (h \cdot \cot (∠ Smaller Acute)))}^{2}}

How to Evaluate Short Diagonal of Trapezoid given Height and Larger Acute Angle?

Short Diagonal of Trapezoid given Height and Larger Acute Angle evaluator uses Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2) to evaluate the Short Diagonal of Trapezoid, Short Diagonal of Trapezoid given Height and Larger Acute Angle 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, and larger acute angle of the Trapezoid. Short Diagonal of Trapezoid is denoted by d_Short symbol.

How to evaluate Short Diagonal of Trapezoid given Height and Larger Acute Angle using this online evaluator? To use this online evaluator for Short Diagonal of Trapezoid given Height and Larger Acute Angle, enter Height of Trapezoid (h), Short Base of Trapezoid (B_Short) & Larger Acute Angle of Trapezoid (∠_{Larger Acute}) and hit the calculate button.

FAQs on Short Diagonal of Trapezoid given Height and Larger Acute Angle

What is the formula to find Short Diagonal of Trapezoid given Height and Larger Acute Angle?

The formula of Short Diagonal of Trapezoid given Height and Larger Acute Angle is expressed as Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2). Here is an example- 11.25149 = sqrt(8^2+(5+(8*cot(1.2217304763958)))^2).

How to calculate Short Diagonal of Trapezoid given Height and Larger Acute Angle?

With Height of Trapezoid (h), Short Base of Trapezoid (B_Short) & Larger Acute Angle of Trapezoid (∠_{Larger Acute}) we can find Short Diagonal of Trapezoid given Height and Larger Acute Angle using the formula - Short Diagonal of Trapezoid = sqrt(Height of Trapezoid^2+(Short Base of Trapezoid+(Height of Trapezoid*cot(Larger Acute Angle of Trapezoid)))^2). This formula also uses Cotangent (cot), Square Root (sqrt) function(s).

What are the other ways to Calculate Short Diagonal of Trapezoid?

Here are the different ways to Calculate Short Diagonal of Trapezoid-

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)))

Can the Short Diagonal of Trapezoid given Height and Larger Acute Angle be negative?

No, the Short Diagonal of Trapezoid given Height and Larger Acute Angle, measured in Length cannot be negative.

Which unit is used to measure Short Diagonal of Trapezoid given Height and Larger Acute Angle?

Short Diagonal of Trapezoid given Height and Larger Acute Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Short Diagonal of Trapezoid given Height and Larger Acute Angle can be measured.

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Short Diagonal of Trapezoid given Height and Larger Acute Angle Formula

​GoShort Diagonal of Trapezoid Formula

​GoShort Diagonal of Trapezoid given Short Leg Formula

Short Diagonal of Trapezoid given Height and Larger Acute Angle Example

Short Diagonal of Trapezoid given Height and Larger Acute Angle Solution

Short Diagonal of Trapezoid given Height and Larger Acute Angle Formula Elements

Other Formulas to find Short Diagonal of Trapezoid

How to Evaluate Short Diagonal of Trapezoid given Height and Larger Acute Angle?

FAQs on Short Diagonal of Trapezoid given Height and Larger Acute Angle

Variable Name

GoShort Diagonal of Trapezoid Formula

GoShort Diagonal of Trapezoid given Short Leg Formula