Right triangle calculator
To calculate the properties of a right triangle when given certain information, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. The theorem can be written as:c2 = a2 + b2
where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
If you know the length of the hypotenuse and one of the other two sides, you can use the Pythagorean theorem to find the length of the remaining side. For example, if you know the length of the hypotenuse is c and the length of one of the legs is a, you can find the length of the other leg by:
b2 = c2 - a2
Additionally, you can use the Pythagorean theorem to find the measure of the angles in a right triangle. You can use the inverse trigonometric functions such as arctan, arcsin, arccos to find the angles.
If you know the side lengths, you can use the trigonometric functions to find the angles:
sin(A) = a/c
cos(A) = b/c
tan(A) = a/b
It's important to note that the Pythagorean theorem holds true only for right triangles. If the triangle is not a right triangle, this theorem will not work.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 the C=90° angle and is the longest side of the triangle and is called the hypotenuse. The symbols a and b are the lengths of the shorter sides, also called legs or arms. Symbols for angles are A (or α alpha) and B (or β beta). Symbol h refers to the altitude (height) of the triangle, which is the length of the perpendicular line segment drawn from the vertex of the triangle to the hypotenuse.
Examples for right triangle calculation:
- two catheti a and b
- cathetus a and hypotenuse c
- cathetus a and opposite angle A
- cathetus a and adjacent angle B
- hypotenuse c and angle A
- hypotenuse c and height h
- area T and hypotenuse c
- area T and cathetus a
- area T and angle A
- circumradius R and cathetus b
- perimeter p and hypotenuse c
- perimeter p and cathetus a
- inradius r and cathetus a
- inradius r and area T
- Medians ma and mb
A right triangle in word problems in mathematics:
- 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? - 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)? - Double ladder
The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach? - Laws
From which law directly follows the validity of Pythagoras' theorem in the right triangle? ... - Know one angle
In a right-angled triangle, the measure of an angle is 40°. Find the measure of other angles of the triangle in degrees.
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