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 α = a/c
cos α = b/c
tan α = 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 m_a and m_b

A right triangle in word problems in mathematics:

• 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)?
• 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.
• Height 40911
  At what height does the 15 m ladder touch the wall if its lower end is 2.5 m away from it?
• 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.

• Vertically 7853
  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.
• A-shaped ladder
  An unfolded double ladder (A-shaped rung) is 10 m long. How high will it reach if the painter extends both parts of the ladder and ensures that the two parts of the ladder are 12 m apart on the ground?
• 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?
• Vector 7
  Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
• Ladder 35331
  The ladder is 13 m long, and its lower part is 5 m away from the wall. How high does the ladder reach?

• Calculate 60423
  In a right triangle RST with a right angle at the vertex T, we know the lengths of two sides: s = 7.8 cm and t = 13 cm; calculate the third party r.
• Height
  Is it true that the height is less or equal to half of the hypotenuse in any right triangle?
• Different 3137
  Mark 4 different points O, P, R. S. Mark of line OP, OR, OS. Measure the marked lines.
• 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?
• Percentage 17613
  At a horizontal distance of 800 m, the ski slope drops to 220 m above sea level. Determine the percentage decrease.

• The supplement
  The supplement of an angle is four times its complement. Find the angle.

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

See triangle basics on Wikipedia or more details on solving triangles.