Right triangle - problemsSee also our right triangle calculator.
The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle.
- Square and circles
Square with sides 41 m is circumscribed and inscribed with circles. Determine the radiuses of both circles.
- 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).