Practice problems of the right triangle - page 32 of 81
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of two of the triangle's sides, which are called the legs of the triangle. The other side of the triangle is called the hypotenuse, which is the side opposite the right angle, and is the longest side of the triangle. Right triangles are important in mathematics and are used in many areas of science and engineering, including trigonometry, physics, and construction. The Pythagorean theorem which states that in a right triangle, the sum of the squares of the legs (a,b) equals the square of the hypotenuse (c) is a fundamental result in geometry.Number of problems found: 1619
- Hexagonal pyramid
Find the area of a shell of the regular hexagonal pyramid if you know that its base edge is 5 cm long and the height of this pyramid is 10 cm. - Triangular prism - regular
The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism. - Solid cuboid
A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Calculate 83261
Calculate the area of the triangle ABC, in which you know the side c=5 cm, the angle at the top A= 70 degrees, and the ratio of the segments cut by the height to the side c is 1:3 - Two cyclists
Two cyclists started crossing at the same time. One goes to the north speed of 20 km/h, the second eastward at a speed of 26 km/h. What will be the direct distance cycling 30 minutes from the start? - Perpendiculars 17003
What is the hole volume drilled by the drill in the shape of a right triangle that revolves around a longer perpendicular? The perpendiculars of the triangle are 10 cm and 3 cm long. - Prism height
What is the prism's height with the base of a right triangle of 6 cm and 9 cm? The diaphragm is 10.8 cm long. The volume of the prism is 58 cm³. Calculate its surface. - Angle of cone
The cone has a base diameter of 1.5 m. The angle at the central apex of the axial section is 86°. Calculate the volume of the cone. - Body diagonal
Calculate the volume of a cuboid whose body diagonal u equals 6.1 cm. The rectangular base has dimensions of 3.2 cm and 2.4 cm. - Pile of sand
A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sandpile is 31 feet. Find the volume of the pile of sand. - Body diagonal
Calculate the cube volume, whose body diagonal size is 75 dm. Draw a picture and highlight the body diagonally. - Pyramid - angle
Calculate the regular quadrangular pyramid's surface whose base edge measured 6 cm, and the deviation from the plane of the base's sidewall plane is 50 degrees. - Sphere and cone
Within the sphere of radius G = 33 cm, inscribe the cone with the largest volume. What is that volume, and what are the dimensions of the cone? - Cone
Calculate the volume and surface area of the cone with a diameter of the base d=15 cm and the side of the cone with the base has angle 52°. - Fighter
A military fighter flies at an altitude of 10 km. The ground position was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h. - Surface 19383 cone
The volume of a cone with a radius of 6 cm is 301.44 cm cubic. What is its surface? - Frustrum - volume, area
Calculate the surface and volume of the truncated cone. The radius of the smaller figure is 4 cm, the height of the cone is 4 cm, and the side of the truncated cone is 5 cm. - Truncated cone 5
The height of a cone is 7 cm, the length of a side is 10 cm, and the lower radius is 3cm. What could be the possible answer for the upper radius of a truncated cone? - Wall height
Calculate the surface and volume of a regular quadrangular pyramid if side a = 6 cm and wall height v = 0.8dm. - Above Earth
To what height must a boy be raised above the earth to see one-fifth of its surface?
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