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 combinations of main and derived properties such as area, perimeter, heights, medians, etc.
Usually by the length of three sides (SSS), side-angle-side, or angle-side-angle.
How does this 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 triangle parameters.
These are successively applied and combined, and the triangle parameters are calculated. Calculator iterates 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. The calculator uses use knowledge, e.g., formulas and relations like the Pythagorean theorem, Sine theorem, Cosine theorem, and Heron's formula. - The second stage is the calculation of the properties of the triangle from the available 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 we know sides b, c, and the 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 we know sides b, c, and the 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 ... altitudes (heights)
ma, mb, mc ... medians
T ... area
p ... perimeter
s ... semiperimeter
Triangles in word problems:
- The sides 7
The sides of the triangle are 5.2, 4.6, and x. If the PERIMETER of the triangle is 11.2 feet, what is the length of the unknown side? (hint: draw a picture) - Triangular 82269
A gardener plants one row of tulips around a triangular bed with sides of 5 m, 6 m, and 10 m. How many tulip bulbs does he need if he wants to plant 8 bulbs on a length of 1 m? - A triangle 10
A triangle has vertices at (4, 5), (-3, 2), and (-2, 5). What are the coordinates of the vertices of the image after the translation (x, y) arrow-right (x + 3, y - 5)? - Intersection 64854
Draw any triangle. Make 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.
- Triangle: 5072
change the triangle in a ratio of 3:4 sides of a triangle: a = 7 cm b = 6 cm c = 5 cm - Triangle 7142
ABC triangle, alpha = 54 degrees 32 minutes, beta = 79 degrees. What are the sizes of the exterior angles? - Circumscribed 29561
Construct an isosceles triangle if a given circle circumscribed with a radius r = 2.6 cm is given. - An isosceles 2
An isosceles triangular frame has a measure of 72 meters on its legs and 18 meters on its base. Find the perimeter of the frame. - Identical 20963
In which triangles is the line identical with the height?
- Construct 25851
A. Construct ∆ABC such that c = 55 mm, α = 45 °, β = 60 °. B. Draw any acute triangle and construct its heights. - Triangle ABC
Construct a triangle ABC is is given c = 60mm hc = 40 mm and b = 48 mm analysis procedure steps construction - Circumference 4420
In an isosceles triangle with a circumference of 36 cm, the height at the base is 12 cm. Calculate the length of the arm of a given triangle. - N points on the side
An equilateral triangle A, B, and 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. - Calculate 6678
You know the size of the two interior angles of the triangle alpha = 40 ° beta = 60 °. Calculate the size of the third interior angle.
The storm broke the vertically growing spruce at 8 meters above the ground. The top fell to the bottom 6 meters from the spruce base. Find the original height of the spruce.more triangle 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
