Goniometry and trigonometry - math word problems - page 27 of 32
Number of problems found: 633
- Quadrilateral prism
The height of a regular quadrilateral prism is v = 10 cm, and the deviation of the body diagonal from the base is 60°. Determine the length of the base edges, the surface, and the prism's volume. - Four sided prism
Calculate the volume and surface area of a regular quadrilateral prism whose height is 28.6 cm, and the diagonal body forms a 50-degree angle with the base plane. - On a mass
Forces F₁ and F₂, each with a magnitude of 40 N, act on a mass point M. Their resultant has a magnitude of 60 N. Determine the angle between forces F₁ and F₂. - Tower
How many m² of the copper plate should be replaced on the roof of the conical tower shape with a diameter 23 m, and the angle at the axial section's vertex is 119°? - Triangle KLB
It is given an equilateral triangle ABC. From point L, the midpoint of the side BC of the triangle, it is drawn perpendicular to the side AB. The intersection of the perpendicular and the side AB is point K. How many percent of the area of the triangle AB - Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at 10° and 100° angles. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and your final answer. - Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30'. - Moon
We see the Moon from the perspective angle 28'. At the time of the full Moon, the Moon's radius is 1740 km. Calculate the mean distance of the Moon from the Earth. - Triangular prism
The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C' has an angle with base 30 degrees, |AB| = 15 cm. Calculate the volume of the prism. - Angle of two lines
There is a regular quadrilateral pyramid ABCDV; | AB | = 4 cm; height v = 6 cm. Determine the angles of lines AD and BV. - Calculate a cone
The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone. - 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. - Glass of juice
A cylindrical glass 13 cm tall with a base diameter of 9 cm is filled with juice to a level 3 cm below the rim. Determine the maximum angle to which the glass can be tilted without the juice spilling. - SSA and geometry
The distance between the points P and Q was 356 m measured in the terrain. The viewer can see the PQ line at a 107°22' viewing angle. The observer's distance from P is 271 m. Find the viewing angle of P and the observer. - Base RR odd
The base of a prism is an isosceles trapezoid ABCD with bases AB = 12 cm and CD = 9 cm. The angle at vertex B is 48°10′. Determine the volume and surface area of the prism if its height is 35 cm. - Distance of points
A regular quadrilateral pyramid ABCDV is given, in which edge AB = a = 4 cm and height v = 8 cm. Let S be the center of the CV. Find the distance of points A and S. - Horizontal Cylindrical Segment
How much fuel is in the horizontal cylindrical segment tank with a length of 10 m, a width of level 1 meter, and a level of 0.2 meters below the tank's upper side? - Spherical sector
The spherical sector has axial section has an angle of α = 120° in the center of the sphere, is part of a sphere with a radius r = 10 cm. Calculate the surface of this spherical sector. - Side edges
The regular 4-sided pyramid has a body height of 2 dm, and the opposite side edges form an angle of 70°. Calculate the surface area and volume of the pyramid. - Two forces 3
Two forces with magnitudes 8 Newtons and 15 Newtons act at a point. Find the angle between the forces if the resultant force is 17 Newtons.
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