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Height of Circular Segment given Chord Length and Central Angle Formula

GoHeight of Circular Segment Formula

GoHeight of Circular Segment given Radius and Central Angle Formula

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Height of Circular Segment is the perpendicular distance of the chord of the Circular Segment from the center of the circle of Circular Segment. Check FAQs

h = \frac{l c}{2} \cdot \cot (- \frac{3}{4} \cdot ∠ Central)

h - Height of Circular Segment?l_c - Chord Length of Circular Segment?∠_Central - Central Angle of Circular Segment?

Height of Circular Segment given Chord Length and Central Angle Example

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Here is how the Height of Circular Segment given Chord Length and Central Angle equation looks like with Values.

Here is how the Height of Circular Segment given Chord Length and Central Angle equation looks like with Units.

Here is how the Height of Circular Segment given Chord Length and Central Angle equation looks like.

5 = \frac{10}{2} \cdot \cot (- \frac{3}{4} \cdot 180)

5m = \frac{10m}{2} \cdot \cot (- \frac{3}{4} \cdot 180°)

5 = \frac{10}{2} \cdot \cot (- \frac{3}{4} \cdot 180)

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Height of Circular Segment given Chord Length and Central Angle Solution

Follow our step by step solution on how to calculate Height of Circular Segment given Chord Length and Central Angle?

FIRST Step Consider the formula

h = \frac{l c}{2} \cdot \cot (- \frac{3}{4} \cdot ∠ Central)

Next Step Substitute values of Variables

∴

h = \frac{10m}{2} \cdot \cot (- \frac{3}{4} \cdot 180°)

Next Step Convert Units

∴

h = \frac{10m}{2} \cdot \cot (- \frac{3}{4} \cdot 3.1416rad)

Next Step Prepare to Evaluate

∴

h = \frac{10}{2} \cdot \cot (- \frac{3}{4} \cdot 3.1416)

Next Step Evaluate

∴

h = 4.99999999999555m

LAST Step Rounding Answer

∴

h = 5m

Height of Circular Segment given Chord Length and Central Angle Formula Elements

Variables

Functions

Height of Circular Segment

Height of Circular Segment is the perpendicular distance of the chord of the Circular Segment from the center of the circle of Circular Segment.

Symbol: h

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Height of Circular Segment

Chord Length of Circular Segment

Chord Length of Circular Segment is the length of the linear boundary edge of a Circular Segment.

Symbol: l_c

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Chord Length of Circular Segment

Central Angle of Circular Segment

Central Angle of Circular Segment is the angle subtended by the arc of a Circular Segment with the center of the circle from which the Circular Segment is cut.

Symbol: ∠_Central

Measurement: AngleUnit: °

Note: Value should be between 0 to 360.

Formulas to find Central Angle of Circular Segment

cot

Cotangent is a trigonometric function that is defined as the ratio of the adjacent side to the opposite side in a right triangle.

Syntax: cot(Angle)

Other Formulas to find Height of Circular Segment

Go Height of Circular Segment

h = r - \sqrt{r^{2} - {(\frac{l c}{2})}^{2}}

Go Height of Circular Segment given Radius and Central Angle

h = r \cdot (1 - \cos (\frac{∠ Central}{2}))

How to Evaluate Height of Circular Segment given Chord Length and Central Angle?

Height of Circular Segment given Chord Length and Central Angle evaluator uses Height of Circular Segment = Chord Length of Circular Segment/2*cot(-3/4*Central Angle of Circular Segment) to evaluate the Height of Circular Segment, Height of Circular Segment given Chord Length and Central Angle formula is defined as the maximum vertical distance of the Circular Segment when the chord of the Circular Segment is the base and calculated using the chord length and central angle of the Circular Segment. Height of Circular Segment is denoted by h symbol.

How to evaluate Height of Circular Segment given Chord Length and Central Angle using this online evaluator? To use this online evaluator for Height of Circular Segment given Chord Length and Central Angle, enter Chord Length of Circular Segment (l_c) & Central Angle of Circular Segment (∠_Central) and hit the calculate button.

FAQs on Height of Circular Segment given Chord Length and Central Angle

What is the formula to find Height of Circular Segment given Chord Length and Central Angle?

The formula of Height of Circular Segment given Chord Length and Central Angle is expressed as Height of Circular Segment = Chord Length of Circular Segment/2*cot(-3/4*Central Angle of Circular Segment). Here is an example- 5 = 10/2*cot(-3/4*3.1415926535892).

How to calculate Height of Circular Segment given Chord Length and Central Angle?

With Chord Length of Circular Segment (l_c) & Central Angle of Circular Segment (∠_Central) we can find Height of Circular Segment given Chord Length and Central Angle using the formula - Height of Circular Segment = Chord Length of Circular Segment/2*cot(-3/4*Central Angle of Circular Segment). This formula also uses Cotangent (cot) function(s).

What are the other ways to Calculate Height of Circular Segment?

Here are the different ways to Calculate Height of Circular Segment-

Height of Circular Segment=Radius of Circular Segment-sqrt(Radius of Circular Segment^2-(Chord Length of Circular Segment/2)^2)
Height of Circular Segment=Radius of Circular Segment*(1-cos(Central Angle of Circular Segment/2))

Can the Height of Circular Segment given Chord Length and Central Angle be negative?

No, the Height of Circular Segment given Chord Length and Central Angle, measured in Length cannot be negative.

Which unit is used to measure Height of Circular Segment given Chord Length and Central Angle?

Height of Circular Segment given Chord Length and Central Angle is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Height of Circular Segment given Chord Length and Central Angle can be measured.

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