Goniometry and trigonometry - math word problems - page 28 of 32
Number of problems found: 633
- Base diagonal
In a regular four-sided pyramid, the side edge forms an angle of 55° with the base's diagonal. The length of the side edge is eight meters. Calculate the pyramid's surface area and volume. - Deviation of the lines
Find the deviation of the lines AG BH in the ABCDEFGH box-cuboid if given | AB | = 3 cm, | AD | = 2 cm, | AE | = 4 cm - Power value
Describe how the instantaneous power value in the AC circuit changes during one period. - Space diagonal angles
Calculate the angle between the body diagonal and the side edge c of the block with dimensions: a = 28 cm, b = 45 cm, and c = 73 cm. Then, find the angle between the body diagonal and the plane of the base ABCD. - Tetrahedral pyramid
Calculate the regular tetrahedral pyramid's volume and surface if the area of the base is 20 cm² and the deviation angle of the side edges from the plane of the base is 60 degrees. - Prism diagonal
The body diagonal of a regular square prism has an angle of 60 degrees with the base, and the edge length is 10 cm. What is the volume of the prism? - Calculate cone
The rotating cone has a base radius r = 226 mm, and the deviation of the side from the base plane is 56°. Calculate the height of the cone. - Angle of deviation
The surface of the rotating cone is 30 cm² (with a circle base), and its surface area is 20 cm². Calculate the deviation of this cone's side from the base's plane. - Deviation - slope angle
Calculate the volume and surface of the rotating cone if its height is 10 cm and the side has a deviation of 30° from the base plane. - Cuboid
Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine the angle between the body diagonal and the base plane (round to degrees). - Sphere submerged in the cone
A right circular cone with a top width of 24 cm and an altitude of 8 cm is filled with water. A spherical steel ball with a radius of 3.0 cm is submerged in the cone. Find the volume of water below the sphere. - Calculate pyramid
Calculate the volume of the pyramid, whose base edge a = 8 cm and the sidewall makes an angle α = 60° with the square base. - 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. - 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. - Quadrilateral prism
Calculate the volume and surface area of a regular quadrilateral prism with base edge a=24 cm if the space diagonal makes an angle of 66° with the base. - Quadrilateral pyramid
The height of a regular quadrilateral pyramid is 6.5 cm, and the angle between the base and the side wall is 42°. Calculate the surface area and volume of the body—round calculations to 1 decimal place. - Quadrilateral oblique prism
What is the volume of a quadrilateral oblique prism with base edges of length a = 1 m, b = 1.1 m, c = 1.2 m, d = 0.7 m if a side edge of length h = 3.9 m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°? - Block
Calculate the volume of a cuboid ABCDEFGH if |AB| = 7 cm, |BC| = 8 cm and the angle ∠CDG = 30.1° - Climb
The road sign that informs the climb is 10.3%—the car drives 10 km along this road. What is the height difference that the car went? - Diagonals of a prism
The base of the square prism is a rectangle with dimensions of 3 dm and 4 dm. The height of the prism is 1 m. Find out the angle between the body diagonal and the base's diagonal.
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