# Right triangle calculator (A,c)

Please enter two properties of the right triangle

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

You have entered hypotenuse c and angle α.

### Right scalene triangle.

Sides: a = 2.07108294825   b = 4.44109081565   c = 4.9

Area: T = 4.59881817698
Perimeter: p = 11.4121737639
Semiperimeter: s = 5.70658688195

Angle ∠ A = α = 25° = 0.4366332313 rad
Angle ∠ B = β = 65° = 1.13444640138 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 4.44109081565
Height: hb = 2.07108294825
Height: hc = 1.87768088856

Median: ma = 4.56600163312
Median: mb = 3.03662396248
Median: mc = 2.45

Vertex coordinates: A[4.9; 0] B[0; 0] C[0.87551703563; 1.87768088856]
Centroid: CG[1.92550567854; 0.62656029619]
Coordinates of the circumscribed circle: U[2.45; -0]
Coordinates of the inscribed circle: I[1.2654960663; 0.80658688195]

Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 155° = 0.4366332313 rad
∠ B' = β' = 115° = 1.13444640138 rad
∠ C' = γ' = 90° = 1.57107963268 rad

# 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).

### 2. From angle α we calculate angle β:

$α + β + 90^\circ = 180^\circ \ \\ β = 90^\circ - α = 90^\circ - 25 ^\circ = 65 ^\circ$

### 4. From cathetus a and hypotenuse c we calculate cathetus b - Pythagorean theorem:

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.

### 6. 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.

$s = \dfrac{ p }{ 2 } = \dfrac{ 11.41 }{ 2 } = 5.71$

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

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.

$T = rs \ \\ r = \dfrac{ T }{ s } = \dfrac{ 4.6 }{ 5.71 } = 0.81$

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.

$R = \dfrac{ c }{ 2 } = \dfrac{ 4.9 }{ 2 } = 2.45$

### 12. 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.

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 Can triangle have two right angles?
• Height 2 Calculate the height of the equilateral triangle with side 38.
• Vector 7 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
• Cable car 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?
• Spruce height How tall was 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?
• Right angled 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?
• Chauncey Chauncey is building a storage bench for his son’s playroom. The storage bench will fit into the corner and against two walls to form a triangle. Chanuncy wants to buy a triangular shaped cover for the bench. If the storage bench is 2 1/2 ft. Along one
• ABS CN Calculate the absolute value of complex number -15-29i.
• Four ropes 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 The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder.
• Right triangle Right triangle legs has lengths 630 mm and 411 dm. Calculate the area of this triangle.
• Triangle ABC In a triangle ABC with the side BC of length 2 cm The middle point of AB. Points L and M split AC side into three equal lines. KLM is isosceles triangle with a right angle at the point K. Determine the lengths of the sides AB, AC triangle ABC.
• 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. 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? 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?