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First Leg of Elliptical Sector Formula

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First Leg of Elliptical Sector is the length of linear edge of the sector which is adjacent to the right most semi major axis of the Elliptical Sector. Check FAQs

l 1 = \sqrt{\frac{{a Sector}^{2} \cdot {b Sector}^{2}}{({a Sector}^{2} \cdot {\sin (∠ Leg(1))}^{2}) + ({b Sector}^{2} \cdot {\cos (∠ Leg(1))}^{2})}}

l₁ - First Leg of Elliptical Sector?a_Sector - Semi Major Axis of Elliptical Sector?b_Sector - Semi Minor Axis of Elliptical Sector?∠_Leg(1) - First Leg Angle of Elliptical Sector?

First Leg of Elliptical Sector Example

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Here is how the First Leg of Elliptical Sector equation looks like with Values.

Here is how the First Leg of Elliptical Sector equation looks like with Units.

Here is how the First Leg of Elliptical Sector equation looks like.

8.3205 = \sqrt{\frac{10^{2} \cdot 6^{2}}{(10^{2} \cdot {\sin (30)}^{2}) + (6^{2} \cdot {\cos (30)}^{2})}}

8.3205m = \sqrt{\frac{{10m}^{2} \cdot {6m}^{2}}{({10m}^{2} \cdot {\sin (30°)}^{2}) + ({6m}^{2} \cdot {\cos (30°)}^{2})}}

8.3205 = \sqrt{\frac{10^{2} \cdot 6^{2}}{(10^{2} \cdot {\sin (30)}^{2}) + (6^{2} \cdot {\cos (30)}^{2})}}

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First Leg of Elliptical Sector Solution

Follow our step by step solution on how to calculate First Leg of Elliptical Sector?

FIRST Step Consider the formula

l 1 = \sqrt{\frac{{a Sector}^{2} \cdot {b Sector}^{2}}{({a Sector}^{2} \cdot {\sin (∠ Leg(1))}^{2}) + ({b Sector}^{2} \cdot {\cos (∠ Leg(1))}^{2})}}

Next Step Substitute values of Variables

∴

l 1 = \sqrt{\frac{{10m}^{2} \cdot {6m}^{2}}{({10m}^{2} \cdot {\sin (30°)}^{2}) + ({6m}^{2} \cdot {\cos (30°)}^{2})}}

Next Step Convert Units

∴

l 1 = \sqrt{\frac{{10m}^{2} \cdot {6m}^{2}}{({10m}^{2} \cdot {\sin (0.5236rad)}^{2}) + ({6m}^{2} \cdot {\cos (0.5236rad)}^{2})}}

Next Step Prepare to Evaluate

∴

l 1 = \sqrt{\frac{10^{2} \cdot 6^{2}}{(10^{2} \cdot {\sin (0.5236)}^{2}) + (6^{2} \cdot {\cos (0.5236)}^{2})}}

Next Step Evaluate

∴

l 1 = 8.32050294337844m

LAST Step Rounding Answer

∴

l 1 = 8.3205m

First Leg of Elliptical Sector Formula Elements

Variables

Functions

First Leg of Elliptical Sector

First Leg of Elliptical Sector is the length of linear edge of the sector which is adjacent to the right most semi major axis of the Elliptical Sector.

Symbol: l₁

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find First Leg of Elliptical Sector

Semi Major Axis of Elliptical Sector

Semi Major Axis of Elliptical Sector is half of the chord passing through both the foci of the Ellipse from which the Elliptical Sector is cut.

Symbol: a_Sector

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Major Axis of Elliptical Sector

Semi Minor Axis of Elliptical Sector

Semi Minor Axis of Elliptical Sector is half of the length of the longest chord which is perpendicular to the line joining the foci of the Ellipse from which the Elliptical Sector is cut.

Symbol: b_Sector

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Semi Minor Axis of Elliptical Sector

First Leg Angle of Elliptical Sector

First Leg Angle of Elliptical Sector is the angle made by the semi major axis on the right and the linear edge of the sector which is adjacent to that semi major axis of the Elliptical Sector.

Symbol: ∠_Leg(1)

Measurement: AngleUnit: °

Note: Value should be between 0 to 180.

Formulas to find First Leg Angle of Elliptical Sector

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)

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: 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.

Syntax: sqrt(Number)

Other formulas in Elliptical Sector category

Go Angle of Elliptical Sector

∠ Sector = ∠ Leg(2) - ∠ Leg(1)

Go First Leg Angle of Elliptical Sector

∠ Leg(1) = ∠ Leg(2) - ∠ Sector

Go Second Leg Angle of Elliptical Sector

∠ Leg(2) = ∠ Sector + ∠ Leg(1)

Go Second Leg of Elliptical Sector

l 2 = \sqrt{\frac{{a Sector}^{2} \cdot {b Sector}^{2}}{({a Sector}^{2} \cdot {\sin (∠ Leg(2))}^{2}) + ({b Sector}^{2} \cdot {\cos (∠ Leg(2))}^{2})}}

How to Evaluate First Leg of Elliptical Sector?

First Leg of Elliptical Sector evaluator uses First Leg of Elliptical Sector = sqrt((Semi Major Axis of Elliptical Sector^2*Semi Minor Axis of Elliptical Sector^2)/((Semi Major Axis of Elliptical Sector^2*sin(First Leg Angle of Elliptical Sector)^2)+(Semi Minor Axis of Elliptical Sector^2*cos(First Leg Angle of Elliptical Sector)^2))) to evaluate the First Leg of Elliptical Sector, First Leg of Elliptical Sector formula is defined as the length of the linear edge of the sector which is adjacent to the rightmost semi-major axis of the Elliptical Sector. First Leg of Elliptical Sector is denoted by l₁ symbol.

How to evaluate First Leg of Elliptical Sector using this online evaluator? To use this online evaluator for First Leg of Elliptical Sector, enter Semi Major Axis of Elliptical Sector (a_Sector), Semi Minor Axis of Elliptical Sector (b_Sector) & First Leg Angle of Elliptical Sector (∠_Leg(1)) and hit the calculate button.

FAQs on First Leg of Elliptical Sector

What is the formula to find First Leg of Elliptical Sector?

The formula of First Leg of Elliptical Sector is expressed as First Leg of Elliptical Sector = sqrt((Semi Major Axis of Elliptical Sector^2*Semi Minor Axis of Elliptical Sector^2)/((Semi Major Axis of Elliptical Sector^2*sin(First Leg Angle of Elliptical Sector)^2)+(Semi Minor Axis of Elliptical Sector^2*cos(First Leg Angle of Elliptical Sector)^2))). Here is an example- 8.320503 = sqrt((10^2*6^2)/((10^2*sin(0.5235987755982)^2)+(6^2*cos(0.5235987755982)^2))).

How to calculate First Leg of Elliptical Sector?

With Semi Major Axis of Elliptical Sector (a_Sector), Semi Minor Axis of Elliptical Sector (b_Sector) & First Leg Angle of Elliptical Sector (∠_Leg(1)) we can find First Leg of Elliptical Sector using the formula - First Leg of Elliptical Sector = sqrt((Semi Major Axis of Elliptical Sector^2*Semi Minor Axis of Elliptical Sector^2)/((Semi Major Axis of Elliptical Sector^2*sin(First Leg Angle of Elliptical Sector)^2)+(Semi Minor Axis of Elliptical Sector^2*cos(First Leg Angle of Elliptical Sector)^2))). This formula also uses Sine (sin)Cosine (cos), Square Root (sqrt) function(s).

Can the First Leg of Elliptical Sector be negative?

No, the First Leg of Elliptical Sector, measured in Length cannot be negative.

Which unit is used to measure First Leg of Elliptical Sector?

First Leg of Elliptical Sector is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which First Leg of Elliptical Sector can be measured.

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First Leg of Elliptical Sector Formula

First Leg of Elliptical Sector Example

First Leg of Elliptical Sector Solution

First Leg of Elliptical Sector Formula Elements

Other formulas in Elliptical Sector category

How to Evaluate First Leg of Elliptical Sector?

FAQs on First Leg of Elliptical Sector

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