Angle D of Cyclic Quadrilateral Calculator

✖Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.ⓘ Side D of Cyclic Quadrilateral [S_d]			+10% -10%
✖Side C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral.ⓘ Side C of Cyclic Quadrilateral [S_c]			+10% -10%
✖Side A of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.ⓘ Side A of Cyclic Quadrilateral [S_a]			+10% -10%
✖Side B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.ⓘ Side B of Cyclic Quadrilateral [S_b]			+10% -10%

✖Angle D of Cyclic Quadrilateral is the space between adjacent sides of Cyclic Quadrilateral, forming angle D.ⓘ Angle D of Cyclic Quadrilateral [∠D]

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Formula

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Angle D of Cyclic Quadrilateral

Formula

`"∠D" = arccos(("S"_{"d"}^2+"S"_{"c"}^2-"S"_{"a"}^2-"S"_{"b"}^2)/(2*(("S"_{"d"}*"S"_{"c"})+("S"_{"b"}*"S"_{"a"}))))`

Example

`"110.7227°"=arccos((("5m")^2+("8m")^2-("10m")^2-("9m")^2)/(2*(("5m"*"8m")+("9m"*"10m"))))`

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Angle D of Cyclic Quadrilateral Solution

STEP 0: Pre-Calculation Summary

Formula Used

Angle D of Cyclic Quadrilateral = arccos((Side D of Cyclic Quadrilateral^2+Side C of Cyclic Quadrilateral^2-Side A of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2)/(2*((Side D of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side A of Cyclic Quadrilateral))))
∠D = arccos((S_d^2+S_c^2-S_a^2-S_b^2)/(2*((S_d*S_c)+(S_b*S_a))))
This formula uses 2 Functions, 5 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)
arccos - Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., arccos(Number)

Variables Used

Angle D of Cyclic Quadrilateral - (Measured in Radian) - Angle D of Cyclic Quadrilateral is the space between adjacent sides of Cyclic Quadrilateral, forming angle D.
Side D of Cyclic Quadrilateral - (Measured in Meter) - Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.
Side C of Cyclic Quadrilateral - (Measured in Meter) - Side C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral.
Side A of Cyclic Quadrilateral - (Measured in Meter) - Side A of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.
Side B of Cyclic Quadrilateral - (Measured in Meter) - Side B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

STEP 1: Convert Input(s) to Base Unit

Side D of Cyclic Quadrilateral: 5 Meter --> 5 Meter No Conversion Required
Side C of Cyclic Quadrilateral: 8 Meter --> 8 Meter No Conversion Required
Side A of Cyclic Quadrilateral: 10 Meter --> 10 Meter No Conversion Required
Side B of Cyclic Quadrilateral: 9 Meter --> 9 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

∠D = arccos((S_d^2+S_c^2-S_a^2-S_b^2)/(2*((S_d*S_c)+(S_b*S_a)))) --> arccos((5^2+8^2-10^2-9^2)/(2*((5*8)+(9*10))))

Evaluating ... ...

∠D = 1.9324764463028

STEP 3: Convert Result to Output's Unit

1.9324764463028 Radian -->110.722744381611 Degree (Check conversion here)

FINAL ANSWER

110.722744381611 ≈ 110.7227 Degree <-- Angle D of Cyclic Quadrilateral

(Calculation completed in 00.004 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Vellore Institute of Technology (VIT), Bhopal

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< 7 Angle of Cyclic Quadrilateral Calculators

Angle between Diagonals of Cyclic Quadrilateral

Go Angle Between Diagonals of Cyclic Quadrilateral = 2*arctan(sqrt(((Semiperimeter of Cyclic Quadrilateral-Side B of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side D of Cyclic Quadrilateral))/((Semiperimeter of Cyclic Quadrilateral-Side A of Cyclic Quadrilateral)*(Semiperimeter of Cyclic Quadrilateral-Side C of Cyclic Quadrilateral))))

Angle A of Cyclic Quadrilateral

Go Angle A of Cyclic Quadrilateral = arccos((Side A of Cyclic Quadrilateral^2+Side D of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2-Side C of Cyclic Quadrilateral^2)/(2*((Side A of Cyclic Quadrilateral*Side D of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral))))

Angle D of Cyclic Quadrilateral

Go Angle D of Cyclic Quadrilateral = arccos((Side D of Cyclic Quadrilateral^2+Side C of Cyclic Quadrilateral^2-Side A of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2)/(2*((Side D of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side A of Cyclic Quadrilateral))))

Angle A of Cyclic Quadrilateral given Angle C

Go Angle A of Cyclic Quadrilateral = pi-Angle C of Cyclic Quadrilateral

Angle D of Cyclic Quadrilateral given Angle B

Go Angle D of Cyclic Quadrilateral = pi-Angle B of Cyclic Quadrilateral

Angle B of Cyclic Quadrilateral

Go Angle B of Cyclic Quadrilateral = pi-Angle D of Cyclic Quadrilateral

Angle C of Cyclic Quadrilateral

Go Angle C of Cyclic Quadrilateral = pi-Angle A of Cyclic Quadrilateral

< 5 Angles of Cyclic Quadrilateral Calculators

Angle between Diagonals of Cyclic Quadrilateral

Angle A of Cyclic Quadrilateral

Angle D of Cyclic Quadrilateral

Angle B of Cyclic Quadrilateral

Go Angle B of Cyclic Quadrilateral = pi-Angle D of Cyclic Quadrilateral

Angle C of Cyclic Quadrilateral

Go Angle C of Cyclic Quadrilateral = pi-Angle A of Cyclic Quadrilateral

Angle D of Cyclic Quadrilateral Formula

What is a Cyclic Quadrilateral?

A Cyclic Quadrilateral is a quadrilateral that can be inscribed in a circle, meaning that there exists a circle that passes through all four vertices of the quadrilateral. Cyclic quadrilaterals are useful in various types of geometry problems, particularly those in which angle chasing is required.

How to Calculate Angle D of Cyclic Quadrilateral?

Angle D of Cyclic Quadrilateral calculator uses Angle D of Cyclic Quadrilateral = arccos((Side D of Cyclic Quadrilateral^2+Side C of Cyclic Quadrilateral^2-Side A of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2)/(2*((Side D of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side A of Cyclic Quadrilateral)))) to calculate the Angle D of Cyclic Quadrilateral, The Angle D of Cyclic Quadrilateral formula is defined as the space between the adjacent sides ( C and D) of Cyclic Quadrilateral, forming angle D. Angle D of Cyclic Quadrilateral is denoted by ∠D symbol.

How to calculate Angle D of Cyclic Quadrilateral using this online calculator? To use this online calculator for Angle D of Cyclic Quadrilateral, enter Side D of Cyclic Quadrilateral (S_d), Side C of Cyclic Quadrilateral (S_c), Side A of Cyclic Quadrilateral (S_a) & Side B of Cyclic Quadrilateral (S_b) and hit the calculate button. Here is how the Angle D of Cyclic Quadrilateral calculation can be explained with given input values -> 6343.946 = arccos((5^2+8^2-10^2-9^2)/(2*((5*8)+(9*10)))).

FAQ

What is Angle D of Cyclic Quadrilateral?

The Angle D of Cyclic Quadrilateral formula is defined as the space between the adjacent sides ( C and D) of Cyclic Quadrilateral, forming angle D and is represented as ∠D = arccos((S_d^2+S_c^2-S_a^2-S_b^2)/(2*((S_d*S_c)+(S_b*S_a)))) or Angle D of Cyclic Quadrilateral = arccos((Side D of Cyclic Quadrilateral^2+Side C of Cyclic Quadrilateral^2-Side A of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2)/(2*((Side D of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side A of Cyclic Quadrilateral)))). Side D of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral, Side C of Cyclic Quadrilateral is one of the four sides of Cyclic Quadrilateral, Side A of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral & Side B of Cyclic Quadrilateral is one of the four sides of the Cyclic Quadrilateral.

How to calculate Angle D of Cyclic Quadrilateral?

The Angle D of Cyclic Quadrilateral formula is defined as the space between the adjacent sides ( C and D) of Cyclic Quadrilateral, forming angle D is calculated using Angle D of Cyclic Quadrilateral = arccos((Side D of Cyclic Quadrilateral^2+Side C of Cyclic Quadrilateral^2-Side A of Cyclic Quadrilateral^2-Side B of Cyclic Quadrilateral^2)/(2*((Side D of Cyclic Quadrilateral*Side C of Cyclic Quadrilateral)+(Side B of Cyclic Quadrilateral*Side A of Cyclic Quadrilateral)))). To calculate Angle D of Cyclic Quadrilateral, you need Side D of Cyclic Quadrilateral (S_d), Side C of Cyclic Quadrilateral (S_c), Side A of Cyclic Quadrilateral (S_a) & Side B of Cyclic Quadrilateral (S_b). With our tool, you need to enter the respective value for Side D of Cyclic Quadrilateral, Side C of Cyclic Quadrilateral, Side A of Cyclic Quadrilateral & Side B of Cyclic Quadrilateral 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 Angle D of Cyclic Quadrilateral?

In this formula, Angle D of Cyclic Quadrilateral uses Side D of Cyclic Quadrilateral, Side C of Cyclic Quadrilateral, Side A of Cyclic Quadrilateral & Side B of Cyclic Quadrilateral. We can use 1 other way(s) to calculate the same, which is/are as follows -

Angle D of Cyclic Quadrilateral = pi-Angle B of Cyclic Quadrilateral

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