Goniometry and trigonometry - math word problems - page 26 of 32
Number of problems found: 634
- 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. - 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. - 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? - 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? - Trapezoid 25 Trapezoid PART with AR||PT has (angle P=x) and (angle A=2x) . In addition, PA = AR = RT = s. Find the length of the median of Trapezoid PART in terms of s.
- Isosceles triangle and cosine
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - 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. - Decagon prism
A regular decagon of side a = 2 cm is the base of the perpendicular prism. The side walls are squares. Find the prism volume in cm³, round to two decimal places. - 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 = 2 m. How many hectoliters of water can fit into the pool? - 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. - Tetrahedral pyramid 8
Let all the side edges of the tetrahedral pyramid ABCDV be equally long and its base let us be a rectangle. Find its volume if you know the deviations A=52° B=56° between the planes of adjacent sidewalls and the base plane. The height of the pyramid is h= - 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? - 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 - 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. - Angle of diagonal
The angle between the body diagonal of a regular quadrilateral and its base is 60°. The edge of the base has a length of 10 cm. Calculate the body volume. - The spacecraft
The spacecraft spotted a radar device at an altitude angle alpha = 34 degrees 37 minutes and had a distance of u = 615 km from Earth's observation point. Calculate the distance d of the spacecraft from Earth at the moment of observation. Earth is consider - Cuboid
Find the dimensions a, b, and c of a cuboid whose space diagonal is d = 6 dm and makes an angle α = 35° with edge a and an angle β = 66° with edge b. - Cross-section of a roof
The owner must cover the carport with a hipped roof with a rectangular cross-section of 8 m x 5 m. All roof surfaces have the same slope of 30°. Determine the price and weight of the roof if 1 m² cost €270 and weighs 43 kg. - The cone
The cone's lateral surface area is 4 cm², and the area of the base is 2 cm². Find the angle in degrees (deviation) of the cone sine and the cone base plane. (The cone side is the segment joining the vertex cone with any point of the base circle. All sides - 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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