Examples for secondary school students - page 228 of 237
Number of problems found: 4730
- Laws
From which law does the validity of Pythagoras' theorem in a right triangle directly follow? ... - Cuboid
A cuboid with edge a = 6 cm and space diagonal u = 31 cm has a volume of V = 900 cm³. Calculate the lengths of the other two edges. - Described
Calculate the circumference of the circle circumscribed about a triangle with sides 82, 495, and 438. - Proof PT
Can Pythagoras' theorem be easily proved using the Euclidean theorems? If so, do it. - Newton's task
Grass grows in the meadow equally fast and evenly. It is known that 35 cows graze meadow for 27 days and 39 cows by 24 days. How many cows graze the meadow for 6 days? - Wire D
A wire of length 6 m is bent to form the perimeter of a semicircle (including the diameter). Determine the radius of the semicircle. - Area of RT
A right triangle has segments on the hypotenuse (created by the altitude) of lengths 15 cm and 9 cm. Determine the area of this triangle. - Square 2
Points D[10,-8] and B[1,-10] are opposite vertices of square ABCD. Calculate the area of square ABCD. - Square
Points A[9,9] and B[-4,1] are adjacent vertices of square ABCD. Calculate the area of square ABCD. - Gimli Glider
A Boeing 767 loses both engines at an altitude of 35000 feet. The captain maintains optimal gliding conditions, losing 2100 feet per minute while maintaining a constant airspeed of 201 knots. Calculate how long it takes for the plane to reach the ground f - Triangle TBC
TBC is an isosceles triangle with base TB, base angle 75°, and equal legs |TC| = |BC| = 35. How long is the base TB? - Cubes
A sphere is inscribed in one cube and the same sphere is circumscribed about another cube. Calculate the difference between the volumes of the two cubes if the difference between their surface areas is 231 cm². - Forces
At point G, three mutually perpendicular forces act: F₁ = 16 N, F₂ = 7 N, and F₃ = 6 N. Determine the resultant force F and the angles between F and each of F₁, F₂, and F₃. - Diagonal
Determine the dimensions of a cuboid whose space diagonal is 60 dm and makes an angle of 35° with one edge and 77° with another edge. - Cone A2V
The lateral surface of a cone, when unrolled flat, forms a circular sector with a central angle of 126° and an area of 415 cm². Calculate the volume of the cone. - Axial section
The axial cross-section of a cone is an equilateral triangle with an area of 208 km². Calculate the volume of the cone. - Rotation
A right triangle with legs 11 cm and 18 cm is rotated around the longer leg. Calculate the volume and surface area of the cone formed. - Right
Determine the angles of a right triangle with hypotenuse c and legs a and b, if: 2a +5b = 5.283c - Euclid3
Calculate the height and sides of the right triangle if one leg is a = 100 km and the section of hypotenuse adjacent to the second leg cb = 14 km. - Euclid2
Right triangle ABC has a right angle at C, with side a = 29 and altitude from C to the hypotenuse h = 17. Calculate the perimeter of the triangle.
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