Right triangle calculator - result

Please enter two properties of the right triangle

Use symbols: a, b, c, A, B, h, T, p, r, R


You have entered cathetus a, cathetus b and hypotenuse c.

Right scalene triangle.

Sides: a = 120   b = 630   c = 641.3276749793

Area: T = 37800
Perimeter: p = 1391.327674979
Semiperimeter: s = 695.6633374897

Angle ∠ A = α = 10.78442978676° = 10°47'3″ = 0.18882215053 rad
Angle ∠ B = β = 79.21657021324° = 79°12'57″ = 1.38325748215 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 630
Height: hb = 120
Height: hc = 117.8810627971

Median: ma = 632.8510693292
Median: mb = 337.0833075814
Median: mc = 320.6633374896

Inradius: r = 54.33766251035
Circumradius: R = 320.6633374896

Vertex coordinates: A[641.3276749793; 0] B[0; 0] C[22.45334529468; 117.8810627971]
Centroid: CG[221.266006758; 39.29435426569]
Coordinates of the circumscribed circle: U[320.6633374896; 0]
Coordinates of the inscribed circle: I[65.66333748965; 54.33766251035]

Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 169.2165702132° = 169°12'57″ = 0.18882215053 rad
∠ B' = β' = 100.7844297868° = 100°47'3″ = 1.38325748215 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle

How did we calculate this triangle?

The calculation of the triangle progress in two phases. The first phase is such that we try to calculate all three sides of the triangle from the input parameters. The first phase is different for the different triangles query entered. The second phase is the calculation of other characteristics of the triangle, such as angles, area, perimeter, heights, the center of gravity, circle radii, etc. Some input data also results in two to three correct triangle solutions (e.g., if the specified triangle area and two sides - typically resulting in both acute and obtuse) triangle).

1. Input data entered: cathetus a, cathetus b and hypotenuse c


Now we know the lengths of all three sides of the triangle, and the triangle is uniquely determined. Next, we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

2. The triangle perimeter is the sum of the lengths of its three sides

3. Semiperimeter of the triangle

The semiperimeter of the triangle is half its perimeter. The semiperimeter frequently appears in formulas for triangles that it is given a separate name. By the triangle inequality, the longest side length of a triangle is less than the semiperimeter.

4. The triangle area - from two legs

5. Calculate the heights of the right triangle from its area.

6. Calculation of the inner angles of the triangle - basic use of sine function

7. Inradius

An incircle of a triangle is a circle which is tangent to each side. An incircle center is called incenter and has a radius named inradius. All triangles have an incenter, and it always lies inside the triangle. The incenter is the intersection of the three angle bisectors. The product of the inradius and semiperimeter (half the perimeter) of a triangle is its area.

8. Circumradius

The circumcircle of a triangle is a circle that passes through all of the triangle's vertices, and the circumradius of a triangle is the radius of the triangle's circumcircle. Circumcenter (center of circumcircle) is the point where the perpendicular bisectors of a triangle intersect.

9. Calculation of medians

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. Every triangle has three medians, and they all intersect each other at the triangle's centroid. The centroid divides each median into parts in the ratio 2:1, with the centroid being twice as close to the midpoint of a side as it is to the opposite vertex. We use Apollonius's theorem to calculate the length of a median from the lengths of its side.


Calculate another triangle

The right triangle calculators compute angles, sides (adjacent, opposite, hypotenuse) and area of any right-angled triangle and use it in the real world. Two independent properties entirely determine any right-angled triangle. The calculator provides a step-by-step explanation for each calculation.

A right triangle is a kind of triangle that has one angle that measures C=90°. In a Right triangle, the side c that is opposite of the C=90° angle, is the longest side of the triangle and is called the hypotenuse. The variables a, b are the lengths of the shorter sides, also called legs or arms. Variables for angles are A, B, or α (alpha) and β (beta). Variable h refers to the altitude(height) of the triangle, which is the length from the vertex C to the hypotenuse of the triangle.

Examples for right triangle calculation:

A right triangle in word problems in mathematics:

  • Triangle P2
    1right_triangle Can triangle have two right angles?
  • Vector 7
    vectors_sum0_1 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
  • Height 2
    1unilateral_triangle Calculate the height of the equilateral triangle with side 38.
  • Right triangle
    right_triangle Right triangle legs has lengths 630 mm and 411 dm. Calculate the area of this triangle.
  • Cableway
    cable-car Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.
  • Broken tree
    stromy_4 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.
  • If the
    tan If the tangent of an angle of a right angled triangle is 0.8. Then its longest side is. .. .
  • Area of RT 2
    tr Calculate the area of right triangle whose legs have a length 5.8 cm and 5.8 cm.
  • Four ropes
    vysilac TV transmitter is anchored at a 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 in the construction of the transmitter. At each attachment
  • RT triangle and height
    345 Calculate the remaining sides of the right triangle if we know side b = 4 cm long and height to side c h = 2.4 cm.
  • ABS CN
    complex_num Calculate the absolute value of complex number -15-29i.
  • Right angled
    right-triangle From the right triangle with legs 12 cm and 20 cm we built a square with the same content as the triangle. How long will be side of the square?
  • Bisectors
    right_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
  • Trapezoid - RR
    right_trapezium Find the area of the right angled trapezoid ABCD with the right angle at the A vertex; a = 3 dm b = 5 dm c = 6 dm d = 4 dm
  • Cable car
    lanovka Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?


next math problems »

Look also our friend's collection of math problems and questions:

See more information about triangles or more details on solving triangles.