# Right triangle calculator (A,a)

Please enter two properties of the right triangle

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

You have entered cathetus a and angle α.

### Right scalene triangle.

Sides: a = 8.34   b = 14.0188279666   c = 16.31215837611

Area: T = 58.45662262072
Perimeter: p = 38.67698634271
Semiperimeter: s = 19.33549317135

Angle ∠ A = α = 30.75° = 30°45' = 0.5376688745 rad
Angle ∠ B = β = 59.25° = 59°15' = 1.03441075818 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 14.0188279666
Height: hb = 8.34
Height: hc = 7.16774494719

Median: ma = 14.62553569117
Median: mb = 10.89442021827
Median: mc = 8.15657918805

Vertex coordinates: A[16.31215837611; 0] B[0; 0] C[4.26441843379; 7.16774494719]
Centroid: CG[6.85985893663; 2.3899149824]
Coordinates of the circumscribed circle: U[8.15657918805; 0]
Coordinates of the inscribed circle: I[5.31766520475; 3.02333479525]

Exterior (or external, outer) angles of the triangle:
∠ A' = α' = 149.25° = 149°15' = 0.5376688745 rad
∠ B' = β' = 120.75° = 120°45' = 1.03441075818 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).

### 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.

$s = \dfrac{ p }{ 2 } = \dfrac{ 38.67 }{ 2 } = 19.33$

### 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.

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.

$R = \dfrac{ c }{ 2 } = \dfrac{ 16.31 }{ 2 } = 8.16$

### 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:

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• Euclid2 In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
• Height Is right that in any right triangle height is less or equal half of the hypotenuse?
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• 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?
• 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.
• 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.
• 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? 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? 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 Cableway has a length of 1800 m. The horizontal distance between the upper and lower cable car station is 1600 m. Calculate how much meters altitude is higher upper station than the base station.