Goniometry and trigonometry - math word problems - page 26 of 32
Number of problems found: 624
- Quadrilateral pyramid
The regular quadrilateral pyramid has a base edge a = 1.56 dm and a height h = 2.05 dm. Calculate: a) the deviation angle of the sidewall plane from the base plane b) deviation angle of the side edge from the plane of the base - Square pyramid
Calculate the pyramid's volume with the side 5 cm long and with a square base, and the side base has an angle of 60 degrees. - Tram - safe downhill
What is the maximum angle at which the tram can go downhill to still be able to stop? The coefficient of shear friction is f =0.15. - An Elizabethan collar
An Elizabethan collar is used to prevent an animal from irritating a wound. The angle between the opening (diameter 6 inches) with a 16-inch diameter and the side of the collar is 53 degrees. Find the surface area of the collar shown. - A missile
A missile is fired with a speed of 100 fps in a direction 30° above the horizontal. Determine the maximum height to which it rises. Fps foot per second. - Flowerbed
The flowerbed has the shape of a truncated pyramid. The bottom edge of the base a = 10 m, and the upper base b = 9 m. The deviation angle between the edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be pl - Acceleration - down a slope
A skier goes down a slope 66 m long in a uniformly accelerated motion in 10 seconds. With what acceleration was it moving, and what is the slope of the slope? - Reflector
The circular reflector throws a light cone with a vertex angle 56° and is on 24 m height tower. The axis of the light beam has the axis of the tower angle 11°. What is the maximum length of the illuminated horizontal plane? - Side wall planes
Find the volume and surface of a cuboid whose side c is 30 cm long and whose body diagonal forms angles of 24°20' and 45°30' with the planes of the side walls. - On a mass
The forces F1, and F2 with magnitudes of 40N act on a mass point M. Their resultant has a magnitude of 60N. Determine the angle that the forces F1 and F2 make. - Circular pool
The pool's base is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length of 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool? - 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. - Diagonal
Determine the dimensions of the cuboid if it is diagonally long 60 dm and has an angle with one edge 35° and with another edge 77°. - The isosceles
The isosceles trapezoid ABCD has bases of 18 cm and 12 cm. The angle at apex A is 60°. What is the circumference and area of the trapezoid? - House volume
V = 35 m α = 55° β = 15° ----------------- X =? Calculate: V- barrack volume =? S- barrack area =? - Isosceles triangle and cosine
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - Four sided prism
Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm, and the diagonal body forms a 50-degree angle with the base plane. - Cone
The rotating cone volume is 9.42 cm3, with a height of 10 cm. What angle is between the side of the cone and its base? - Chimney
The lower circumference of the chimney is 12.57 m, and the top circumference is 5.655 m. The slope of the walls is 87°. Find the height of the chimney. - Truncated pyramid
Find the volume of a regular 4-sided truncated pyramid if a1 = 14 cm, a2 = 8 cm, and the angle that the side wall with the base is 42 degrees.
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