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:
- Triangle P2
Can a triangle have two right angles? - Calculate
Calculate the area of the ABE triangle AB = 38mm and height E = 42mm ps: please try a quick calculation - Diagonal
Can it be a diagonal diamond twice longer than its side? - Height of right RT
The right triangle ABC has a hypotenuse c 9 cm long and a part of the hypotenuse cb = 3 cm. How long is the height of this right triangle? - Intersection 64854
Draw any triangle. The axis of its two sides. Their intersection is point S. (a) Measure the distance of point S from all three vertices b) Draw the axis of the third party. - Area of RT 2
Calculate the area of a right triangle whose legs have a length of 5.8 cm and 5.8 cm. - The triangles
The triangles ABC and A'B'C 'are similar with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '. - The farmer
The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th - Euclid2
In the right triangle ABC with a right angle at C is given side a=29 and height v=17. Calculate the perimeter of the triangle. - Broken tree
The tree is broken at 4 meters above the ground and the top of the tree touches the ground at a distance of 5 from the trunk. Calculate the original height of the tree. - 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? - Calculate 2556
Calculate the arm size b of the trapezoid ABCD if a = 12 cm, c = 4 cm, d (AC) = d (BC) and the area S (triangle ABC) = 9 cm square. - Diagonal
Can a rhombus have the same length, diagonal, and side? - Laws
From which law directly follows the validity of Pythagoras' theorem in the right triangle? ... - Triangle ABC
Construct a triangle ABC is is given c = 60mm hc = 40 mm and b = 48 mm analysis procedure steps construction
more math problems »
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
