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:
- Triangle and axes
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. - 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) - 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)? - 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?
- 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. - 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 - angles
ABC triangle, alpha = 54 degrees 32 minutes, beta = 79 degrees. What are the sizes of the exterior angles? - Diagonal
Can a rhombus have the same length, diagonal, and side? - Probability 4824
We have five lines with lengths of 3cm, 5cm, 7cm, 9cm, and 11cm. What is the probability that we will be able to construct a triangle with randomly selected three?
- 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. - A triangle 8
A triangle has a base of 9.2 feet and a height of 4.8 feet. What is the area of the triangle? - Projection 3493
In axonometry, construct a projection of an oblique circular cone with a base in a plane. The stop triangle gives dimension. We know the center of the base S, the radius of the base ra the top of the cone V, Triangle (6,7,6), S (2,0,4), V (-2,7,6), r = 3 - Right-angled 3511
In a right-angled triangle at vertex C, the alpha angle is 24 degrees smaller than the beta angle to determine the size of the triangle angles. - Perpendiculars 46081
Calculate the size of the hypotenuse in a triangle if its perpendiculars are 8 cm and 8.4 cm long.
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
