Triangle calculator
The calculator solves the triangle specified by three of its properties. Each triangle has six main characteristics: three sides a, b, c, and three angles (α, β, γ). The classic trigonometry problem is to specify three of these six characteristics and find the other three. Of course, our calculator solves triangles from any combinations of main and derived properties such as area, perimeter, heights, medians, etc.
Usually by the length of three sides (SSS) or side-angle-side or angle-side-angle.
How does this triangle calculator solve a triangle?
The calculation of the general triangle has two phases:- The expert phase is different for different tasks. The calculator tries to calculate the sizes of three sides of the triangle from the entered data. He gradually applies the knowledge base to the entered data, which is represented in particular by the relationships between individual parameters of the triangle.
These are successively applied and combined, and the parameters of the triangle calculate. Calculator iterate until the triangle has calculated all three sides.
For example, the appropriate height is calculated from the given area of the triangle and the corresponding side. From the known height and angle, the adjacent side, etc., can be calculated. They use knowledge, e.g., formulas (relations) Pythagorean theorem, Sine theorem, Cosine theorem, Heron's formula, solving equations and systems of equations. - The second stage is the calculation of the properties of the triangle from the known lengths of its three sides.
Examples of how to enter a triangle:
a=3 b=4 c=5 ... triangle calc by three sides a,b,c.
B=45 c=10 a=9 ... triangle calc by two sides a,c and included angle B.
A=25 C=80 b=22
A=35 C=26 a=10
a=3 C=90 c=5 ... how to enter right-angled triangle.
a=3 β=25 γ=45 ... triangle calc if we know the side and two angles.
a=3 β=25 T=12 ... triangle calc, if know side, angle, and area of a triangle.
T=2.5 c=2 b=4 ... find side a if know sides b, c, and area of triangle T.
ma=1 b=2.5 c=2 ... calculation of the triangle if we know one median and any two sides.
ma=1 mb=2.5 mc=2 ... triangle calc by three medians.
ha=220, hb=165 hc=132 ... triangle calc by three heights.
a=7 β=40 mc=5 ... triangle calc by one side, one angle, and one median.
a:b:c=2:3:4 T=2.5 ... a triangle where the known side ratio, and its area.
A:B:C=1:4:5 a=2 ... calculating triangle if we know the ratio of the internal angles and one side.
B=45 c=10 a=9 ... triangle calc by two sides a,c and included angle B.
A=25 C=80 b=22
A=35 C=26 a=10
a=3 C=90 c=5 ... how to enter right-angled triangle.
a=3 β=25 γ=45 ... triangle calc if we know the side and two angles.
a=3 β=25 T=12 ... triangle calc, if know side, angle, and area of a triangle.
T=2.5 c=2 b=4 ... find side a if know sides b, c, and area of triangle T.
ma=1 b=2.5 c=2 ... calculation of the triangle if we know one median and any two sides.
ma=1 mb=2.5 mc=2 ... triangle calc by three medians.
ha=220, hb=165 hc=132 ... triangle calc by three heights.
a=7 β=40 mc=5 ... triangle calc by one side, one angle, and one median.
a:b:c=2:3:4 T=2.5 ... a triangle where the known side ratio, and its area.
A:B:C=1:4:5 a=2 ... calculating triangle if we know the ratio of the internal angles and one side.
What do the symbols mean?
a, b, c ... sides BC, AC, AB
A, B, C or α, β, γ ... internal angles
ha, hb, hc ... heights
ma, mb, mc ... medians
T ... area
p ... perimeter
s ... semiperimeter
Triangles in word problems:
- Center traverse
Does the middle traverse indeed bisect the triangle? - Triangle P2
Can a triangle have two right angles? - Diagonal
Can be a diagonal of diamond twice longer than it side? - Draw a
Draw a triangle ABC, if you know: alpha = 60° side b = 4 cm side a = 10 cm - Triangle ABC
Construct a triangle ABC is is given c = 60mm hc = 40 mm and b = 48 mm analysis procedure steps construction - QuizQ
An isosceles triangle has two sides of length 7 km and 39 km. How long is a third side? - Sides of triangle
Triangle circumference with two identical sides is 117cm. The third side measures 44cm. How many cms do you measure one of the same sides? - Approximation of tangent fx
What is the non-trig formula (not a polynomial fit) for the growth curve that solves algebraically for the increase between tan(1 degree), tan( 2 degrees) continuing up to tangent(45 degrees)? okay to use pi Check calculation for 12° - A triangle 3
A triangle has base 5 5/6 feet and height 7 2/5 feet. Find the area of the triangle as a mixed number. - In triangle
In triangle ABC, the magnitude of the internal angle gamma is equal to one-third of the angle alpha. The size of the angle beta is 80 degrees larger than the size of the gamma angle. Calculate the magnitudes of the interior angles of the triangle ABC. - Similarity coefficient
The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ". - Construction
Construction the triangle ABC, if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60° and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction) - N points on the side
There is an equilateral triangle A, B, C on each of its inner sides lies N=13 points. Find the number of all triangles whose vertices lie at given points on different sides. - Medians 2:1
Median to side b (tb) in triangle ABC is 12 cm long. a. What is the distance of the center of gravity T from the vertex B? b, Find the distance between T and the side b. - Find the
Find the third interior angle of the triangle ABC where: α = 48°, γ = 65°.
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Look also at our friend's collection of math problems and questions:
- triangle
- right triangle
- Heron's formula
- The Law of Sines
- The Law of Cosines
- Pythagorean theorem
- triangle inequality
- similarity of triangles
- The right triangle altitude theorem
