Triangle practice problems - page 64 of 126
Number of problems found: 2520
- Rotation of the Earth
Calculate the linear speed of the Earth's surface at a latitude of 34.5°. Assume a globe with a radius of 6378 km. - Find radius
Find the radius of the circle using the Pythagorean theorem where a=9, b=r, c= 6+r - RT and circles
Solve the right triangle if the radius of the inscribed circle is r=9 and the radius of the circumscribed circle is R=26. - Parabola focus equation
Determine the equation of the parabola that has the point F = [3,2] as its focus and the line x+y+1=0 as its shift line. - Distance
What is the distance between the origin and the point (-11; 13)? - Perimeter and diagonal
The perimeter of the rectangle is 82 m, and the length of its diagonal is 29 m. Find the dimensions of the rectangle. - Determine the surface area
Find the surface area of a cone of height 30 cm whose slant side makes an angle of 60° with the base plane. - CoG center
Find the position of the center of gravity of a system of four mass points having masses, m1, m2 = 2 m1, m3 = 3 m1, and m4 = 4 m1, if they lie at the vertices of an isosceles tetrahedron. (in all case - Martians
A sphere-shaped spaceship with a diameter of 6 m landed in the meadow. To avoid attracting attention, the Martians covered it with a roof in the shape of a regular cone. How high will this roof be so that the consumption of roofing is minimal? - Spherical section cut
Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 degrees. - Cuboid face diagonals
The lengths of the cuboid edges are in the ratio 1:2:3. Will the lengths of its diagonals be in the same ratio? The cuboid has dimensions of 5 cm, 10 cm, and 15 cm. Calculate the size of the wall diagonals of this cuboid. - Weight of Gold Pyramid
The teacher cast the gold in the shape of a regular triangular pyramid with a base edge length of 12 cm and a height of 8 cm. The density of gold is 19,320 kg/m³. What is the weight of the casting? - Rotary bodies
The rotating cone and the rotary cylinder have the same volume of 180 cm³ and the same height, v = 15 cm. Which of these two bodies has a larger surface area? - Diagonals
Draw a square ABCD whose diagonals have a length of 6 cm. - Thales
Calculate the length of the Thales' circle described to the right triangle with hypotenuse 44.2 cm. - Triangle cone volume
Calculate the volume of the cone formed by rotating an isosceles triangle about the height of the base. The triangle has a side length of 15 cm and a height to the base of 12 cm. When calculating, use the value pi = 3.14 and round the result to one decima - Triangular pyramid
Calculate the volume of a regular triangular pyramid with edge length a = 12 cm and pyramid height v = 20 cm. - Tangent spheres
A sphere with a radius of 1 m is placed in the corner of the room. What is the largest sphere size that fits into the corner behind it? Additional info: Two spheres are placed in the corner of a room. The spheres are each tangent to the walls and floor an - Sphere from tree points
Equation of sphere with three-point (a,0,0), (0, a,0), (0,0, a) and center lies on plane x+y+z=a - Floating barrel
A barrel (cylindrical in shape) floats on water with its top 18 dm above the water surface. The width of the part of the barrel above the waterline is 34 dm. The length of the barrel is 12 dm. Calculate the volume of the barrel.
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