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? - 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? - Diagonal
Can it be a diagonal diamond twice longer than its side? - 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. - Calculate
Calculate the area of the ABE triangle AB = 38mm and height E = 42mm ps: please try a quick calculation - Right angled
We built a square with the same area as the right triangle with legs 12 cm and 20 cm. How long will be the side of the square? - Area of a triangle
Find the area of a triangle with a base of 7 mm and a height of 10 mm? - Similarity of triangles
If triangle ABC ~ to triangle XYZ, AC = 24, AB = 15, BC = 17, and XY = 9, what is the perimeter of triangle XYZ? Round all sides to 1 decimal place. - Find the
Find the third interior angle of the triangle ABC where: α = 48°, γ = 65°. - 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? - Four ropes
TV transmitter is anchored at the height of 44 meters by four ropes. Each rope is attached at a distance of 55 meters from the heel of the TV transmitter. Calculate how many meters of rope were used to construct the transmitter. At each attachment is need - Construction
Construct 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) - Ladder
The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder. - Triangle ABC
In a triangle ABC with the side BC of length 2 cm. Point K is the middle point of AB. Points L and M split the AC side into three equal lines. KLM is an isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triang - 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.
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
