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Angle of Elevation

Solves angle of elevation word problems

Angle Ratio for a Triangle

Given an angle ratio for a triangle of a:b:c, this determines the angle measurements of the triangle.

Cevian Triangle Relations

Given a triangle with a cevian, this will solve for the cevian or segments or sides based on inputs

Clock Angle

Calculate the angle on a clock between the hour and minute hands or how many times on the clock form an angle of (x°) between the minute and hour hand (backwards and forwards)

Complementary and Supplementary Angles

This calculator determines the complementary and supplementary angle of a given angle that you enter OR it checks to see if two angles that you enter are complementary or supplementary.

Equilateral Triangle

Given a side (a), this calculates the following items of the equilateral triangle:

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h_{a},h_{b},h_{c})

* medians (m_{a},m_{b},m_{c})

* angle bisectors (t_{a},t_{b},t_{c})

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

* Perimeter (P)

* Semi-Perimeter (s)

* Area (A)

* altitudes (h

* medians (m

* angle bisectors (t

* Circumscribed Circle Radius (R)

* Inscribed Circle Radius (r)

Geometric Mean of a Triangle

Given certain segments of a special right triangle, this will calculate other segments using the geometric mean

Isosceles Triangle

Given a long side (a) and a short side (b), this determines the following items of the isosceles triangle:

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

* Area (A)

* Semi-Perimeter (s)

* Altitude a (ha)

* Altitude b (hb)

* Altitude c (hc)

Kites

This calculates perimeter and/or area of a kite given certain inputs such as short and long side, short and long diagonal, or angle between short and long side

Line Equation-Slope-Distance-Midpoint-Y intercept

Enter 2 points, and this calculates the following:

* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points

* Midpoint of the two points

* Distance between the 2 points

* 2 remaining angles of the rignt triangle formed by the 2 points

* y intercept of the line equation

* Point-Slope Form

* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points

* Midpoint of the two points

* Distance between the 2 points

* 2 remaining angles of the rignt triangle formed by the 2 points

* y intercept of the line equation

* Point-Slope Form

* Parametric Equations and Symmetric Equations

Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.

Also allows for the entry of m and b to form the line equation

Pascal-Floyd-Leibniz Triangle

This generates the first (n) rows of the following triangles:

Pascal's Triangle

Leibniz's Harmonic Triangle

Floyd's Triangle

Pascal's Triangle

Leibniz's Harmonic Triangle

Floyd's Triangle

Polar Conics

Given eccentricity (e), directrix (d), and angle θ, this determines the vertical and horizontal directrix polar equations.

Polygon Side

Determines the sides of a polygon given an interior angle sum.

Polygons

Using various input scenarios of a polygon such as side length, number of sides, apothem, and radius, this calculator determines Perimeter or a polygon and Area of the polygon.
This also determines interior angles of a polygon and diagonals of a polygon as well as the total number of 1 vertex diagonals.

Pythagorean Theorem

Figures out based on user entry the missing side or missing hypotenuse of a right triangle. In addition, the calculator shows the proof of the Pythagorean Theorem and then determines by numerical evaluation if the 2 sides and hypotenuse you entered are a right triangle using the Pythagorean Theorem

Pythagorean Theorem Trig Proofs

Shows the proof of 3 pythagorean theorem related identities using the angle θ:

Sin^{2}(θ) + Cos^{2}(θ) = 1

Tan^{2}(θ) + 1 = Sec^{2}(θ)

Sin(θ)/Cos(θ) = Tan(θ)

Sin

Tan

Sin(θ)/Cos(θ) = Tan(θ)

Quadrilateral

Given 4 points entered, this determines the area using Brahmaguptas Formula and perimeter of the quadrilateral formed by the points as well as checking to see if the quadrilateral (quadrangle) is a parallelogram.

Rectangle Word Problem

Solves word problems based on area or perimeter and variable side lengths

Rectangles and Parallelograms

Solve for Area, Perimeter, length, and width of a rectangle or parallelogram and also calculates the diagonal length as well as the circumradius and inradius.

Reference Angle

Calculates the reference angle for a given angle.

Right Triangles

This solves for all the pieces of a right triangle based on given inputs using items like the sin ratio, cosine ratio, tangent ratio, and the Pythagorean Theorem as well as the inradius.

Special Triangles: Isosceles and 30-60-90

Given an Isosceles triangle (45-45-90) or 30-60-90 right triangle, the calculator will solve the 2 remaining sides of the triangle given one side entered.

Sum to Product and Product to Sum Formulas

Given two angles in degrees of u and v, this determines the following:

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

* Sin(u) ± Sin(v)

* Cos(u) ± Cos(v)

* Sin(u)Sin(v)

* Cos(u)Cos(v)

* Sin(u)Cos(v)

* Cos(u)Sin(v)

* Sin(u + v)

* Sin(u - v)

* Cos(u + v)

* Cos(u - v)

* Tan(u + v)

* Tan(u - v)

Triangle Coordinate Items

Enter 3 points for the vertices of a triangle, and this will calculate the area of that triangle and the centroid.

Triangle Inequality

This calculator displays 2 scenarios

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

1) Enter 3 sides of a triangle, and it will determine if the side lengths satisfy the properties of the triangle inequality and form a triangle

2) Enter 2 sides of a triangle, and this will determine an acceptable range for the length of the 3rd side of a triangle so that the 3rd side respects the Triangle Inequality.

Triangle Solver and Classify Triangles

Solves a triangle including area using the following solving methods

Side-Angle-Side (SAS)

Angle-Side-Angle (ASA)

Side-Side-Angle (SSA)

Side-Side-Side (SSS)

Area (A) is solved using Herons Formula

Law of Sines

Law of Cosines

Also classifies triangles based on sides and angles entered.

Side-Angle-Side (SAS)

Angle-Side-Angle (ASA)

Side-Side-Angle (SSA)

Side-Side-Side (SSS)

Area (A) is solved using Herons Formula

Law of Sines

Law of Cosines

Also classifies triangles based on sides and angles entered.

Trig Angle conversions

Converts between degrees, radians, gradians, revolutions, and quadrants.

Trig Measurement

Given an angle θ, this calculates the following measurements:

Sin(θ) = Sine

Cos(θ) = Cosine

Tan(θ) = Tangent

Csc(θ) = Cosecant

Sec(θ) = Secant

Cot(θ) = Cotangent

Arcsin(x) = θ = Arcsine

Arccos(x) = θ = Arccosine

Arctan(x) =θ = Arctangent

Also converts between Degrees and Radians and Gradians

Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined.

Sin(θ) = Sine

Cos(θ) = Cosine

Tan(θ) = Tangent

Csc(θ) = Cosecant

Sec(θ) = Secant

Cot(θ) = Cotangent

Arcsin(x) = θ = Arcsine

Arccos(x) = θ = Arccosine

Arctan(x) =θ = Arctangent

Also converts between Degrees and Radians and Gradians

Coterminal Angles as well as determine if it is acute, obtuse, or right angle. For acute angles, a cofunction will be determined.

Trigonometry Summary

This is a list of important angle formulas and identities in trigonometry

Vectors

Given 2 vectors A and B, this calculates:

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj_{B}A and and the vector component of A orthogonal to B → A - proj_{B}A

Also calculates the horizontal component and vertical component of a 2-D vector.

* Length (magnitude) of A = ||A||

* Length (magnitude) of B = ||B||

* Sum of A and B = A + B (addition)

* Difference of A and B = A - B (subtraction)

* Dot Product of vectors A and B = A x B

A ÷ B (division)

* Distance between A and B = AB

* Angle between A and B = θ

* Unit Vector U of A.

* Determines the relationship between A and B to see if they are orthogonal (perpendicular), same direction, or parallel (includes parallel planes).

* Cauchy-Schwarz Inequality

* The orthogonal projection of A on to B, proj

Also calculates the horizontal component and vertical component of a 2-D vector.

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A man stands at point p, 45 metres from the base of a building that is 20 metres high. Find the angl

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Triangle with perimeter

Triangle with perimeter

The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimete

The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee

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Finding the dimensions

Help on problem

Help on problem

the length of a rectangular map is 15 inches and the perimeter is 50 inches. Find the width

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The circle has an arc measure of 180 degrees

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