Pythagorean theorem - problemsPythagorean theorem is the base for the right triangle calculator.
- Square and circles
Square with sides 82 km is circumscribed and inscribed with circles. Determine the radiuses of both circles.
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 ?
It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a1 = 6 cm and a2 = 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
- 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?
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 va=13 cm, vb=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.
In the middle of a cylindrical tank with a bottom diameter 350 cm is standing rod which is 31 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
- 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.
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.
- Circle chord
Determine the radius of the circle in which the chord 18 cm away from the center of the circle is 28 cm longer than the radius of the circle.
- Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
- Concentric circles
In the circle with diameter 17 cm is constructed chord 12 cm long. Calculate the radius of a concentric circle that touches this chord.
- Tetrahedral pyramid
It is given a regular tetrahedral pyramid with base edge 6 cm and the height of the pyramid 10 cm. Calculate the length of its side edges.