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Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid. Check FAQs
h=dLongdShortBLong+BShortsin(d(Leg))
h - Height of Trapezoid?dLong - Long Diagonal of Trapezoid?dShort - Short Diagonal of Trapezoid?BLong - Long Base of Trapezoid?BShort - Short Base of Trapezoid?d(Leg) - Leg Angle between Diagonals of Trapezoid?

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

With values
With units
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Here is how the Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals equation looks like with Values.

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

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

8.2724Edit=14Edit12Edit15Edit+5Editsin(80Edit)
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Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals Solution

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

FIRST Step Consider the formula
h=dLongdShortBLong+BShortsin(d(Leg))
Next Step Substitute values of Variables
h=14m12m15m+5msin(80°)
Next Step Convert Units
h=14m12m15m+5msin(1.3963rad)
Next Step Prepare to Evaluate
h=141215+5sin(1.3963)
Next Step Evaluate
h=8.27238512530216m
LAST Step Rounding Answer
h=8.2724m

Height of Trapezoid given Both Diagonals and Leg 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.
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: dLong
Measurement: LengthUnit: m
Note: Value should be greater than 0.
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: dShort
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Long Base of Trapezoid
Long Base of Trapezoid is the longer side among the pair of parallel sides of the Trapezoid.
Symbol: BLong
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Short Base of Trapezoid
Short Base of Trapezoid is the shorter side among the pair of parallel sides of the Trapezoid.
Symbol: BShort
Measurement: LengthUnit: m
Note: Value should be greater than 0.
Leg Angle between Diagonals of Trapezoid
Leg Angle between Diagonals of Trapezoid is the angle made by the diagonals of the Trapezoid which is near to any of the pair of non parallel and opposite legs of the Trapezoid.
Symbol: d(Leg)
Measurement: AngleUnit: °
Note: Value should be between 0 to 180.
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=LLong2-((BLong-BShort)2+LLong2-LShort22(BLong-BShort))2
​Go Height of Trapezoid given Long Leg
h=LLongsin(Smaller Acute)
​Go Height of Trapezoid given Short Leg
h=LShortsin(Larger Acute)
​Go Height of Trapezoid given Area
h=2ABLong+BShort

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

Height of Trapezoid given Both Diagonals and Leg 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(Leg Angle between Diagonals of Trapezoid) to evaluate the Height of Trapezoid, Height of Trapezoid given Both Diagonals and Leg 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 leg angle between diagonals of the Trapezoid. Height of Trapezoid is denoted by h symbol.

How to evaluate Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals using this online evaluator? To use this online evaluator for Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals, enter Long Diagonal of Trapezoid (dLong), Short Diagonal of Trapezoid (dShort), Long Base of Trapezoid (BLong), Short Base of Trapezoid (BShort) & Leg Angle between Diagonals of Trapezoid (∠d(Leg)) and hit the calculate button.

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

What is the formula to find Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals?
The formula of Height of Trapezoid given Both Diagonals and Leg 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(Leg Angle between Diagonals of Trapezoid). Here is an example- 8.272385 = (14*12)/(15+5)*sin(1.3962634015952).
How to calculate Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals?
With Long Diagonal of Trapezoid (dLong), Short Diagonal of Trapezoid (dShort), Long Base of Trapezoid (BLong), Short Base of Trapezoid (BShort) & Leg Angle between Diagonals of Trapezoid (∠d(Leg)) we can find Height of Trapezoid given Both Diagonals and Leg 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(Leg 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)OpenImg
  • Height of Trapezoid=Long Leg of Trapezoid*sin(Smaller Acute Angle of Trapezoid)OpenImg
  • Height of Trapezoid=Short Leg of Trapezoid*sin(Larger Acute Angle of Trapezoid)OpenImg
Can the Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals be negative?
No, the Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals, measured in Length cannot be negative.
Which unit is used to measure Height of Trapezoid given Both Diagonals and Leg Angle between Diagonals?
Height of Trapezoid given Both Diagonals and Leg 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 Leg Angle between Diagonals can be measured.
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