Pythagorean theorem - problems - page 2
Points A[1,5] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 18 km/h, the second at average speed 24 km/h. Determine the distance between them after 30 minutes cycling.
- Gimli Glider
Aircraft Boeing 767 lose both engines at 45000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2080 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
- Short cut
Imagine that you are going to the friend. That path has a length 330 meters. Then turn doprava and go another 840 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
From the observatory 18 m high and 26 m from the river bank, river width appears in the visual angle φ = 14°30'. Calculate width of the river.
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
- Cube diagonal
Determine length of the cube diagonal with edge 55 dm.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 137 cm2.
Calculate the perimeter and area of rhombus whose diagonals are 26 cm and 42 cm long.
Trunk diameter is 79 cm. Is it possible to inscribe a square prism with side 75 cm?
- Square and circles
Square with sides 89 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.
In rectangle with sides 10 and 9 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
- Rhombus ABCD
Rhombus ABCD, |AC| = 42 cm, |BD| = 96 cm. Calculate the perimeter of the rhombus ABCD.
Calculate the length of the diagonal of the rectangle ABCD with sides a = 6 cm, b = 7 cm.
- Widescreen monitor
Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of the LCD monitor with a diagonal size 37 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha
In point X acts three orthogonal forces: F1 = 13 N, F2 = 8 N and F3 = 15 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
- 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 ?
- Square diagonal
Calculate length of the square diagonal if the perimeter is 200 cm.
- MO SK/CZ Z9–I–3
John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
Pythagorean theorem is the base for the right triangle calculator.