Diagonal of Isosceles Trapezoid given Long Base and Acute Angle Calculator

✖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%
✖Lateral Edge of Isosceles Trapezoid is the length of the pair of opposite and non parallel edges of the Isosceles Trapezoid.ⓘ Lateral Edge of Isosceles Trapezoid [l_e(Lateral)]			+10% -10%
✖Acute Angle of Isosceles Trapezoid is any of the angles on the longer base edge made with the lateral and non parallel edges of the Isosceles Trapezoid.ⓘ Acute Angle of Isosceles Trapezoid [∠_Acute]			+10% -10%

✖Diagonal of Isosceles Trapezoid is the length of the line joining any pair of opposite corners of the Isosceles Trapezoid.ⓘ Diagonal of Isosceles Trapezoid given Long Base and Acute Angle [d]

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Diagonal of Isosceles Trapezoid given Long Base and Acute Angle Solution

STEP 0: Pre-Calculation Summary

Formula Used

Diagonal of Isosceles Trapezoid = sqrt(Long Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2-(2*Long Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Acute Angle of Isosceles Trapezoid)))
d = sqrt(B_Long^2+l_e(Lateral)^2-(2*B_Long*l_e(Lateral)*cos(∠_Acute)))
This formula uses 2 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(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., sqrt(Number)

Variables Used

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.
Lateral Edge of Isosceles Trapezoid - (Measured in Meter) - Lateral Edge of Isosceles Trapezoid is the length of the pair of opposite and non parallel edges of the Isosceles Trapezoid.
Acute Angle of Isosceles Trapezoid - (Measured in Radian) - Acute Angle of Isosceles Trapezoid is any of the angles on the longer base edge made with the lateral and non parallel edges of the Isosceles Trapezoid.

STEP 1: Convert Input(s) to Base Unit

Long Base of Isosceles Trapezoid: 15 Meter --> 15 Meter No Conversion Required
Lateral Edge of Isosceles Trapezoid: 5 Meter --> 5 Meter No Conversion Required
Acute Angle of Isosceles Trapezoid: 55 Degree --> 0.959931088596701 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

d = sqrt(B_Long^2+l_e(Lateral)^2-(2*B_Long*l_e(Lateral)*cos(∠_Acute))) --> sqrt(15^2+5^2-(2*15*5*cos(0.959931088596701)))

Evaluating ... ...

d = 12.8048246589839

STEP 3: Convert Result to Output's Unit

12.8048246589839 Meter --> No Conversion Required

FINAL ANSWER

12.8048246589839 ≈ 12.80482 Meter <-- Diagonal of Isosceles Trapezoid

(Calculation completed in 00.004 seconds)

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< Diagonal of Isosceles Trapezoid Calculators

Diagonal of Isosceles Trapezoid given Short Base and Obtuse Angle

LaTeX Go Diagonal of Isosceles Trapezoid = sqrt(Short Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2-(2*Short Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Obtuse Angle of Isosceles Trapezoid)))

Diagonal of Isosceles Trapezoid given Short Base and Acute Angle

LaTeX Go Diagonal of Isosceles Trapezoid = sqrt(Short Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2+(2*Short Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Acute Angle of Isosceles Trapezoid)))

Diagonal of Isosceles Trapezoid given Long Base and Obtuse Angle

LaTeX Go Diagonal of Isosceles Trapezoid = sqrt(Long Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2+(2*Long Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Obtuse Angle of Isosceles Trapezoid)))

Diagonal of Isosceles Trapezoid given Long Base and Acute Angle

LaTeX Go Diagonal of Isosceles Trapezoid = sqrt(Long Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2-(2*Long Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Acute Angle of Isosceles Trapezoid)))

Diagonal of Isosceles Trapezoid given Long Base and Acute Angle 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 Diagonal of Isosceles Trapezoid given Long Base and Acute Angle?

Diagonal of Isosceles Trapezoid given Long Base and Acute Angle calculator uses Diagonal of Isosceles Trapezoid = sqrt(Long Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2-(2*Long Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Acute Angle of Isosceles Trapezoid))) to calculate the Diagonal of Isosceles Trapezoid, Diagonal of Isosceles Trapezoid given Long Base and Acute Angle formula is defined as the length of the line joining any pair of opposite corners of the Isosceles Trapezoid, and calculated using long base and acute angle of the Isosceles Trapezoid. Diagonal of Isosceles Trapezoid is denoted by d symbol.

How to calculate Diagonal of Isosceles Trapezoid given Long Base and Acute Angle using this online calculator? To use this online calculator for Diagonal of Isosceles Trapezoid given Long Base and Acute Angle, enter Long Base of Isosceles Trapezoid (B_Long), Lateral Edge of Isosceles Trapezoid (l_e(Lateral)) & Acute Angle of Isosceles Trapezoid (∠_Acute) and hit the calculate button. Here is how the Diagonal of Isosceles Trapezoid given Long Base and Acute Angle calculation can be explained with given input values -> 12.80482 = sqrt(15^2+5^2-(2*15*5*cos(0.959931088596701))).

FAQ

What is Diagonal of Isosceles Trapezoid given Long Base and Acute Angle?

Diagonal of Isosceles Trapezoid given Long Base and Acute Angle formula is defined as the length of the line joining any pair of opposite corners of the Isosceles Trapezoid, and calculated using long base and acute angle of the Isosceles Trapezoid and is represented as d = sqrt(B_Long^2+l_e(Lateral)^2-(2*B_Long*l_e(Lateral)*cos(∠_Acute))) or Diagonal of Isosceles Trapezoid = sqrt(Long Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2-(2*Long Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Acute Angle of Isosceles Trapezoid))). Long Base of Isosceles Trapezoid is the longer side among the pair of parallel sides of the Isosceles Trapezoid, Lateral Edge of Isosceles Trapezoid is the length of the pair of opposite and non parallel edges of the Isosceles Trapezoid & Acute Angle of Isosceles Trapezoid is any of the angles on the longer base edge made with the lateral and non parallel edges of the Isosceles Trapezoid.

How to calculate Diagonal of Isosceles Trapezoid given Long Base and Acute Angle?

Diagonal of Isosceles Trapezoid given Long Base and Acute Angle formula is defined as the length of the line joining any pair of opposite corners of the Isosceles Trapezoid, and calculated using long base and acute angle of the Isosceles Trapezoid is calculated using Diagonal of Isosceles Trapezoid = sqrt(Long Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2-(2*Long Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Acute Angle of Isosceles Trapezoid))). To calculate Diagonal of Isosceles Trapezoid given Long Base and Acute Angle, you need Long Base of Isosceles Trapezoid (B_Long), Lateral Edge of Isosceles Trapezoid (l_e(Lateral)) & Acute Angle of Isosceles Trapezoid (∠_Acute). With our tool, you need to enter the respective value for Long Base of Isosceles Trapezoid, Lateral Edge of Isosceles Trapezoid & Acute Angle 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 Diagonal of Isosceles Trapezoid?

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

Diagonal of Isosceles Trapezoid = sqrt(Long Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2+(2*Long Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Obtuse Angle of Isosceles Trapezoid)))
Diagonal of Isosceles Trapezoid = sqrt(Short Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2-(2*Short Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Obtuse Angle of Isosceles Trapezoid)))
Diagonal of Isosceles Trapezoid = sqrt(Short Base of Isosceles Trapezoid^2+Lateral Edge of Isosceles Trapezoid^2+(2*Short Base of Isosceles Trapezoid*Lateral Edge of Isosceles Trapezoid*cos(Acute Angle of Isosceles Trapezoid)))

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