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)?
• 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?
• 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.
• Vector 7
  Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
• Trapezoid - RR
  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
• Six-sided polygon
  There is a six-sided polygon. The first two angles are equal, the third angle is twice (the equal angles), two other angles are trice the equal angle, while the last angle is a right angle. Find the value of each angle.
• Broken tree
  The tree is broken at 4 meters above the ground. The top of the tree touches the ground at a distance of 5 meters from the trunk. Calculate the original height of the tree.
• Calculate ΔRST
  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 side r.
• Spruce height
  How tall was the spruce that was cut at an altitude of 8m above the ground, and the top landed at a distance of 15m from the heel of the tree?
• Centimeter 64224
  A ladder leans against the wall. It touches the wall at the height of 340 cm, and its lower end is 160 cm away from the wall. How long is the ladder? Express the result to the nearest centimeter.
• Bisector 2
  ABC is an isosceles triangle. While AB=AC, AX is the bisector of the angle ∢BAC meeting side BC at X. Prove that X is the midpoint of BC.
• Distance 4527
  There are two points, K and L, KL = 4 cm. Draw a line p passing through point K and having a distance of 4 cm from point L.
• RT triangle and height
  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.
• Interior 39791
  For the interior angles of a triangle, the angle β is twice as large, and the angle γ is three times larger than the angle α. Is this triangle right?
• Right triangle - legs
  Calculate the area of a right-angled triangle ABC with a=15 cm, b=1.7 dm.

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Also, take a look 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.