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Height of Trapezoid given Both Diagonals and Base Angle between Diagonals Formula

GoHeight of Trapezoid Formula

GoHeight of Trapezoid given Long Leg Formula

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

h = \frac{d Long \cdot d Short}{B Long + B Short} \cdot \sin (∠ d(Base))

h - Height of Trapezoid?d_Long - Long Diagonal of Trapezoid?d_Short - Short Diagonal of Trapezoid?B_Long - Long Base of Trapezoid?B_Short - Short Base of Trapezoid?∠_d(Base) - Base Angle between Diagonals of Trapezoid?

Height of Trapezoid given Both Diagonals and Base Angle between Diagonals Example

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Here is how the Height of Trapezoid given Both Diagonals and Base Angle between Diagonals equation looks like with Values.

Here is how the Height of Trapezoid given Both Diagonals and Base Angle between Diagonals equation looks like with Units.

Here is how the Height of Trapezoid given Both Diagonals and Base Angle between Diagonals equation looks like.

8.2724 = \frac{14 \cdot 12}{15 + 5} \cdot \sin (100)

8.2724m = \frac{14m \cdot 12m}{15m + 5m} \cdot \sin (100°)

8.2724 = \frac{14 \cdot 12}{15 + 5} \cdot \sin (100)

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Height of Trapezoid given Both Diagonals and Base Angle between Diagonals Solution

Follow our step by step solution on how to calculate Height of Trapezoid given Both Diagonals and Base Angle between Diagonals?

FIRST Step Consider the formula

h = \frac{d Long \cdot d Short}{B Long + B Short} \cdot \sin (∠ d(Base))

Next Step Substitute values of Variables

∴

h = \frac{14m \cdot 12m}{15m + 5m} \cdot \sin (100°)

Next Step Convert Units

∴

h = \frac{14m \cdot 12m}{15m + 5m} \cdot \sin (1.7453rad)

Next Step Prepare to Evaluate

∴

h = \frac{14 \cdot 12}{15 + 5} \cdot \sin (1.7453)

Next Step Evaluate

∴

h = 8.27238512530303m

LAST Step Rounding Answer

∴

h = 8.2724m

Height of Trapezoid given Both Diagonals and Base Angle between Diagonals Formula Elements

Variables

Functions

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

Long Diagonal of Trapezoid

Long Diagonal of Trapezoid is the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the Trapezoid.

Symbol: d_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Diagonal of Trapezoid

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

Long Base of Trapezoid

Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.

Symbol: B_Long

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Long Base 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

Base Angle between Diagonals of Trapezoid

Base Angle between Diagonals of Trapezoid is the angle made by the diagonals of the Trapezoid which is near to any of the pair of parallel and opposite base edges of the Trapezoid.

Symbol: ∠_d(Base)

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find Base Angle between Diagonals of Trapezoid

sin

Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse.

Syntax: sin(Angle)

Other Formulas to find Height of Trapezoid

Go Height of Trapezoid

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

Go Height of Trapezoid given Long Leg

h = L Long \cdot \sin (∠ Smaller Acute)

Go Height of Trapezoid given Short Leg

h = L Short \cdot \sin (∠ Larger Acute)

Go Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals

h = \frac{d Long \cdot d Short}{B Long + B Short} \cdot \sin (∠ d(Leg))

How to Evaluate Height of Trapezoid given Both Diagonals and Base Angle between Diagonals?

Height of Trapezoid given Both Diagonals and Base Angle between Diagonals evaluator uses Height of Trapezoid = (Long Diagonal of Trapezoid*Short Diagonal of Trapezoid)/(Long Base of Trapezoid+Short Base of Trapezoid)*sin(Base Angle between Diagonals of Trapezoid) to evaluate the Height of Trapezoid, Height of Trapezoid given Both Diagonals and Base Angle between Diagonals formula is defined as the perpendicular distance between the pair of parallel sides of the Trapezoid, and calculated using both diagonals and base angle between diagonals of the Trapezoid. Height of Trapezoid is denoted by h symbol.

How to evaluate Height of Trapezoid given Both Diagonals and Base Angle between Diagonals using this online evaluator? To use this online evaluator for Height of Trapezoid given Both Diagonals and Base Angle between Diagonals, enter Long Diagonal of Trapezoid (d_Long), Short Diagonal of Trapezoid (d_Short), Long Base of Trapezoid (B_Long), Short Base of Trapezoid (B_Short) & Base Angle between Diagonals of Trapezoid (∠_d(Base)) and hit the calculate button.

FAQs on Height of Trapezoid given Both Diagonals and Base Angle between Diagonals

What is the formula to find Height of Trapezoid given Both Diagonals and Base Angle between Diagonals?

The formula of Height of Trapezoid given Both Diagonals and Base Angle between Diagonals is expressed as Height of Trapezoid = (Long Diagonal of Trapezoid*Short Diagonal of Trapezoid)/(Long Base of Trapezoid+Short Base of Trapezoid)*sin(Base Angle between Diagonals of Trapezoid). Here is an example- 8.272385 = (14*12)/(15+5)*sin(1.745329251994).

How to calculate Height of Trapezoid given Both Diagonals and Base Angle between Diagonals?

With Long Diagonal of Trapezoid (d_Long), Short Diagonal of Trapezoid (d_Short), Long Base of Trapezoid (B_Long), Short Base of Trapezoid (B_Short) & Base Angle between Diagonals of Trapezoid (∠_d(Base)) we can find Height of Trapezoid given Both Diagonals and Base Angle between Diagonals using the formula - Height of Trapezoid = (Long Diagonal of Trapezoid*Short Diagonal of Trapezoid)/(Long Base of Trapezoid+Short Base of Trapezoid)*sin(Base Angle between Diagonals of Trapezoid). This formula also uses Sine (sin) function(s).

What are the other ways to Calculate Height of Trapezoid?

Here are the different ways to Calculate Height of Trapezoid-

Height of Trapezoid=sqrt(Long Leg of Trapezoid^2-(((Long Base of Trapezoid-Short Base of Trapezoid)^2+Long Leg of Trapezoid^2-Short Leg of Trapezoid^2)/(2*(Long Base of Trapezoid-Short Base of Trapezoid)))^2)
Height of Trapezoid=Long Leg of Trapezoid*sin(Smaller Acute Angle of Trapezoid)
Height of Trapezoid=Short Leg of Trapezoid*sin(Larger Acute Angle of Trapezoid)

Can the Height of Trapezoid given Both Diagonals and Base Angle between Diagonals be negative?

No, the Height of Trapezoid given Both Diagonals and Base Angle between Diagonals, measured in Length cannot be negative.

Which unit is used to measure Height of Trapezoid given Both Diagonals and Base Angle between Diagonals?

Height of Trapezoid given Both Diagonals and Base Angle between Diagonals is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Trapezoid given Both Diagonals and Base Angle between Diagonals can be measured.

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Height of Trapezoid given Both Diagonals and Base Angle between Diagonals Formula

​GoHeight of Trapezoid Formula

​GoHeight of Trapezoid given Long Leg Formula

Height of Trapezoid given Both Diagonals and Base Angle between Diagonals Example

Height of Trapezoid given Both Diagonals and Base Angle between Diagonals Solution

Height of Trapezoid given Both Diagonals and Base Angle between Diagonals Formula Elements

Other Formulas to find Height of Trapezoid

How to Evaluate Height of Trapezoid given Both Diagonals and Base Angle between Diagonals?

FAQs on Height of Trapezoid given Both Diagonals and Base Angle between Diagonals

Variable Name

GoHeight of Trapezoid Formula

GoHeight of Trapezoid given Long Leg Formula