# Right triangle - problems

See also our right triangle calculator.- Square and circles

Square with sides 82 km is circumscribed and inscribed with circles. Determine the radiuses of both circles. - Rectangle

The rectangle is 36 cm long and 48 cm wide. Determine the radius of the circle circumscribing rectangle. - Proof PT

Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it. - Square diagonal

Calculate length of the square diagonal if the perimeter is 200 cm. - Reverse Pythagorean theorem

Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 73 m, 66 m, 51 m ? Δ DEF: 63 cm, 105 cm, 84 cm ? Δ GHI: 50 dm, 48 dm, 14 dm ? Δ JKL: 31 m, 45 m, 40 m ? Δ MNO: 28 m, 53 m, 45 m ? - Rhombus

It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 6 cm and a_{2}= 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Kites

Boys run kite on a cable of 86 meters long. What is the kite altitude, if the angle from the horizontal plane is 77°? - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 236 dm. - 4s pyramid

Regular tetrahedral pyramid has a base edge a=6 and collaterally edge length b=15. What is its height? - n-gon II

What is the side length of the regular 9-gon circumscribed circle of radius 13 cm? - Crossroads

The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car. - Floating barrel

Barrel (cylinder shape) floats on water, top of barrel is 7 dm above water and the width of surfaced barrel part is 20 dm. Barrel length is 27 dm. Calculate the volume of the barrel. - Triangle and its heights

Calculate the length of the sides of the triangle ABC, if v_{a}=13 cm, v_{b}=17 cm and side b is 5 cm shorter than side a. - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Triangle TBC

TBC is isosceles triangle with base TB with base angle 52° and legs length |TC| = |BC| = 30. How long is the base TB? - Aircraft

The plane flies at altitude 6800 m. At the time of first measurement was to see the elevation angle of 20° and second measurement of the elevation angle of 34°. Calculate the distance the plane flew between the two measurements. - Hexagonal pyramid

Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm. - Triangle

Calculate the area of the triangle ABC if b = c = 20 cm, R = 21 cm (R is the circumradius). - Diamond

Side length of diamond is 35 cm and the length of the diagonal is 56 cm. Calculate the height and length of the second diagonal. - Climb

For horizontal distance 3 km road rise by 5.4 m. Calculate the road pitch in ‰ (permille, parts per thousand).

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