Height of Isosceles Trapezoid given Diagonal Calculator

✖Diagonal of Isosceles Trapezoid is the length of the line joining any pair of opposite corners of the Isosceles Trapezoid.ⓘ Diagonal of Isosceles Trapezoid [d]			+10% -10%
✖Long Base of Isosceles Trapezoid is the longer side among the pair of parallel sides of the Isosceles Trapezoid.ⓘ Long Base of Isosceles Trapezoid [B_Long]			+10% -10%
✖Short Base of Isosceles Trapezoid is the shorter side among the pair of parallel sides of the Isosceles Trapezoid.ⓘ Short Base of Isosceles Trapezoid [B_Short]			+10% -10%
✖Obtuse Angle of Diagonals of Isosceles Trapezoid is the angle made by the diagonals of the Isosceles Trapezoid which is greater than 90 degree.ⓘ Obtuse Angle of Diagonals of Isosceles Trapezoid [∠_d(Obtuse)]			+10% -10%

✖Height of Isosceles Trapezoid is the perpendicular distance between the pair of parallel base edges of the Isosceles Trapezoid.ⓘ Height of Isosceles Trapezoid given Diagonal [h]

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Height of Isosceles Trapezoid given Diagonal Solution

STEP 0: Pre-Calculation Summary

Formula Used

Height of Isosceles Trapezoid = (Diagonal of Isosceles Trapezoid^2)/(Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)*sin(Obtuse Angle of Diagonals of Isosceles Trapezoid)
h = (d^2)/(B_Long+B_Short)*sin(∠_d(Obtuse))
This formula uses 1 Functions, 5 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 Isosceles Trapezoid - (Measured in Meter) - Height of Isosceles Trapezoid is the perpendicular distance between the pair of parallel base edges of the Isosceles Trapezoid.
Diagonal of Isosceles Trapezoid - (Measured in Meter) - Diagonal of Isosceles Trapezoid is the length of the line joining any pair of opposite corners of the Isosceles Trapezoid.
Long Base of Isosceles Trapezoid - (Measured in Meter) - Long Base of Isosceles Trapezoid is the longer side among the pair of parallel sides of the Isosceles Trapezoid.
Short Base of Isosceles Trapezoid - (Measured in Meter) - Short Base of Isosceles Trapezoid is the shorter side among the pair of parallel sides of the Isosceles Trapezoid.
Obtuse Angle of Diagonals of Isosceles Trapezoid - (Measured in Radian) - Obtuse Angle of Diagonals of Isosceles Trapezoid is the angle made by the diagonals of the Isosceles Trapezoid which is greater than 90 degree.

STEP 1: Convert Input(s) to Base Unit

Diagonal of Isosceles Trapezoid: 13 Meter --> 13 Meter No Conversion Required
Long Base of Isosceles Trapezoid: 15 Meter --> 15 Meter No Conversion Required
Short Base of Isosceles Trapezoid: 9 Meter --> 9 Meter No Conversion Required
Obtuse Angle of Diagonals of Isosceles Trapezoid: 140 Degree --> 2.4434609527916 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

h = (d^2)/(B_Long+B_Short)*sin(∠_d(Obtuse)) --> (13^2)/(15+9)*sin(2.4434609527916)

Evaluating ... ...

h = 4.52629608487854

STEP 3: Convert Result to Output's Unit

4.52629608487854 Meter --> No Conversion Required

FINAL ANSWER

4.52629608487854 ≈ 4.526296 Meter <-- Height of Isosceles Trapezoid

(Calculation completed in 00.008 seconds)

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< Height of Isosceles Trapezoid Calculators

Height of Isosceles Trapezoid given Diagonal

LaTeX Go Height of Isosceles Trapezoid = (Diagonal of Isosceles Trapezoid^2)/(Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)*sin(Obtuse Angle of Diagonals of Isosceles Trapezoid)

Height of Isosceles Trapezoid given Long and Short Base

LaTeX Go Height of Isosceles Trapezoid = ((Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid)/2)*tan(Acute Angle of Isosceles Trapezoid)

Height of Isosceles Trapezoid given Lateral Edge and Obtuse Angle

LaTeX Go Height of Isosceles Trapezoid = Lateral Edge of Isosceles Trapezoid*sin(Obtuse Angle of Isosceles Trapezoid)

Height of Isosceles Trapezoid given Lateral Edge and Acute Angle

LaTeX Go Height of Isosceles Trapezoid = Lateral Edge of Isosceles Trapezoid*sin(Acute Angle of Isosceles Trapezoid)

Height of Isosceles Trapezoid given Diagonal Formula

LaTeX Go

What is an Isosceles Trapezoid?

A Trapezoid is a quadrilateral with one pair of parallel edges. An Isosceles Trapezoid means a trapezoid with the pair of non parallel edges are equal. The parallel pair of edges are called bases and the pair of non parallel equal edges are called lateral edges. The angles on the long base are equal acute angles and the angles on the short base are equal obtuse angles. Also, the pair of opposite angles are supplementary to each other. And hence an Isosceles Trapezoid is cyclic.

How to Calculate Height of Isosceles Trapezoid given Diagonal?

Height of Isosceles Trapezoid given Diagonal calculator uses Height of Isosceles Trapezoid = (Diagonal of Isosceles Trapezoid^2)/(Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)*sin(Obtuse Angle of Diagonals of Isosceles Trapezoid) to calculate the Height of Isosceles Trapezoid, Height of Isosceles Trapezoid given Diagonal formula is defined as the perpendicular distance between the pair of parallel base edges of the Isosceles Trapezoid, and calculated using diagonal of the Isosceles Trapezoid. Height of Isosceles Trapezoid is denoted by h symbol.

How to calculate Height of Isosceles Trapezoid given Diagonal using this online calculator? To use this online calculator for Height of Isosceles Trapezoid given Diagonal, enter Diagonal of Isosceles Trapezoid (d), Long Base of Isosceles Trapezoid (B_Long), Short Base of Isosceles Trapezoid (B_Short) & Obtuse Angle of Diagonals of Isosceles Trapezoid (∠_d(Obtuse)) and hit the calculate button. Here is how the Height of Isosceles Trapezoid given Diagonal calculation can be explained with given input values -> 4.526296 = (13^2)/(15+9)*sin(2.4434609527916).

FAQ

What is Height of Isosceles Trapezoid given Diagonal?

Height of Isosceles Trapezoid given Diagonal formula is defined as the perpendicular distance between the pair of parallel base edges of the Isosceles Trapezoid, and calculated using diagonal of the Isosceles Trapezoid and is represented as h = (d^2)/(B_Long+B_Short)*sin(∠_d(Obtuse)) or Height of Isosceles Trapezoid = (Diagonal of Isosceles Trapezoid^2)/(Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)*sin(Obtuse Angle of Diagonals of Isosceles Trapezoid). Diagonal of Isosceles Trapezoid is the length of the line joining any pair of opposite corners of the Isosceles Trapezoid, Long Base of Isosceles Trapezoid is the longer side among the pair of parallel sides of the Isosceles Trapezoid, Short Base of Isosceles Trapezoid is the shorter side among the pair of parallel sides of the Isosceles Trapezoid & Obtuse Angle of Diagonals of Isosceles Trapezoid is the angle made by the diagonals of the Isosceles Trapezoid which is greater than 90 degree.

How to calculate Height of Isosceles Trapezoid given Diagonal?

Height of Isosceles Trapezoid given Diagonal formula is defined as the perpendicular distance between the pair of parallel base edges of the Isosceles Trapezoid, and calculated using diagonal of the Isosceles Trapezoid is calculated using Height of Isosceles Trapezoid = (Diagonal of Isosceles Trapezoid^2)/(Long Base of Isosceles Trapezoid+Short Base of Isosceles Trapezoid)*sin(Obtuse Angle of Diagonals of Isosceles Trapezoid). To calculate Height of Isosceles Trapezoid given Diagonal, you need Diagonal of Isosceles Trapezoid (d), Long Base of Isosceles Trapezoid (B_Long), Short Base of Isosceles Trapezoid (B_Short) & Obtuse Angle of Diagonals of Isosceles Trapezoid (∠_d(Obtuse)). With our tool, you need to enter the respective value for Diagonal of Isosceles Trapezoid, Long Base of Isosceles Trapezoid, Short Base of Isosceles Trapezoid & Obtuse Angle of Diagonals of Isosceles 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 Isosceles Trapezoid?

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

Height of Isosceles Trapezoid = Lateral Edge of Isosceles Trapezoid*sin(Obtuse Angle of Isosceles Trapezoid)
Height of Isosceles Trapezoid = Lateral Edge of Isosceles Trapezoid*sin(Acute Angle of Isosceles Trapezoid)
Height of Isosceles Trapezoid = ((Long Base of Isosceles Trapezoid-Short Base of Isosceles Trapezoid)/2)*tan(Acute Angle of Isosceles Trapezoid)

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