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

✖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 [d_Long]			+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 [d_Short]			+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%
✖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%
✖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.ⓘ Base Angle between Diagonals of Trapezoid [∠_d(Base)]			+10% -10%

✖Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.ⓘ Height of Trapezoid given Both Diagonals and Base Angle between Diagonals [h]

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

STEP 0: Pre-Calculation Summary

Formula Used

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)
h = (d_Long*d_Short)/(B_Long+B_Short)*sin(∠_d(Base))
This formula uses 1 Functions, 6 Variables

Functions Used

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., sin(Angle)

Variables Used

Height of Trapezoid - (Measured in Meter) - Height of Trapezoid is the perpendicular distance between the pair of parallel sides of the Trapezoid.
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.
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.
Long Base of Trapezoid - (Measured in Meter) - Long Base of Trapezoid is the longer side among 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.
Base Angle between Diagonals of Trapezoid - (Measured in Radian) - 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.

STEP 1: Convert Input(s) to Base Unit

Long Diagonal of Trapezoid: 14 Meter --> 14 Meter No Conversion Required
Short Diagonal of Trapezoid: 12 Meter --> 12 Meter No Conversion Required
Long Base of Trapezoid: 15 Meter --> 15 Meter No Conversion Required
Short Base of Trapezoid: 5 Meter --> 5 Meter No Conversion Required
Base Angle between Diagonals of Trapezoid: 100 Degree --> 1.745329251994 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (d_Long*d_Short)/(B_Long+B_Short)*sin(∠_d(Base)) --> (14*12)/(15+5)*sin(1.745329251994)

Evaluating ... ...

h = 8.27238512530303

STEP 3: Convert Result to Output's Unit

8.27238512530303 Meter --> No Conversion Required

FINAL ANSWER

8.27238512530303 ≈ 8.272385 Meter <-- Height of Trapezoid

(Calculation completed in 00.008 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Indian Institute of Technology (IIT), Mumbai

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< Height of Trapezoid Calculators

Height of Trapezoid

LaTeX Go 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 given Both Diagonals and Base Angle between Diagonals

LaTeX Go 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)

Height of Trapezoid given Short Leg

LaTeX Go Height of Trapezoid = Short Leg of Trapezoid*sin(Larger Acute Angle of Trapezoid)

Height of Trapezoid given Long Leg

LaTeX Go Height of Trapezoid = Long Leg of Trapezoid*sin(Smaller Acute Angle of Trapezoid)

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

LaTeX Go

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

Height of Trapezoid given Both Diagonals and Base Angle between Diagonals calculator 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 calculate 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 calculate Height of Trapezoid given Both Diagonals and Base Angle between Diagonals using this online calculator? To use this online calculator 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. Here is how the Height of Trapezoid given Both Diagonals and Base Angle between Diagonals calculation can be explained with given input values -> 8.272385 = (14*12)/(15+5)*sin(1.745329251994).

FAQ

What is Height of Trapezoid given Both Diagonals and Base Angle between Diagonals?

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 and is represented as h = (d_Long*d_Short)/(B_Long+B_Short)*sin(∠_d(Base)) or 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). Long Diagonal of Trapezoid is the length of the line joining the corners of smaller acute angle and smaller obtuse angle of the 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, Long Base of Trapezoid is the longer side among 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 & 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.

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

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 is calculated using 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 calculate Height of Trapezoid given Both Diagonals and Base Angle between Diagonals, you need 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)). With our tool, you need to enter the respective value for Long Diagonal of Trapezoid, Short Diagonal of Trapezoid, Long Base of Trapezoid, Short Base of Trapezoid & Base Angle between Diagonals 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 Height of Trapezoid?

In this formula, Height of Trapezoid uses Long Diagonal of Trapezoid, Short Diagonal of Trapezoid, Long Base of Trapezoid, Short Base of Trapezoid & Base Angle between Diagonals of Trapezoid. We can use 3 other way(s) to calculate the same, which is/are as follows -

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)

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