Right triangle - problemsSee 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.
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.
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?
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.
- 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?
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.
Calculate the area of the triangle ABC if b = c = 20 cm, R = 21 cm (R is the circumradius).
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.
For horizontal distance 3 km road rise by 5.4 m. Calculate the road pitch in ‰ (permille, parts per thousand).