# Right triangle calculator

Please enter two properties of the right triangle

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

c

^{2}= a

^{2}+ b

^{2}

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:

b

^{2}= c

^{2}- a

^{2}

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 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? - Euclid2

The ABC right triangle with a right angle at C is side a=29 and height v=17. Calculate the perimeter of the triangle. - 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. - Double ladder

The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart? - Calculate 83265

Calculate the area of a right-angled triangle ABC with a=15 cm, b=1.7 dm. - Calculate

Calculate the length of a side of the equilateral triangle with an area of 50cm². - 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? - Area of RT 2

Calculate the area of a right triangle whose legs have a length of 6.2 cm and 9.8 cm. - 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 - 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. - 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. - Laws

From which law directly follows the validity of Pythagoras' theorem in the right triangle? ... - 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?

more triangle problems »

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

- triangle
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- The Law of Sines
- The Law of Cosines
- Pythagorean theorem
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