Goniometry and trigonometry - math word problems - page 29 of 30
Number of problems found: 596
- House volume
V = 35 m α = 55° β = 15° ----------------- X =? Calculate: V- barrack volume =? S- barrack area =?
- Cube - angles
Calculate the angle alpha (α) between the wall diagonal and cube base. Calculate the angle beta (β) between the cube body diagonal and the cube base.
- Aircraft climbing
The average climb angle of the aircraft is 11° 20', and its average speed is 400 km/h. How long does it take to climb to a height of 3000m?
- Determine 4876
The rotating cone has a height of 72 cm and an angle at the top of 72 °. Determine the volume of the sphere.
- Raindrops
The car runs on a horizontal track at a constant speed of 20 m2-1. It is raining. Raindrops fall in a vertical direction at a speed of 6 m/s. a) How fast is the speed of the drops relative to the car windows? b) What is the angle of the raindro
- Perpendicular direction
A speedboat moves relative to the water at a constant speed of 13 m/s. The speed of the water current in the river is 5 m/s a) At what angle concerning the water current must the boat sail to keep moving perpendicular to the banks of the river? b) At what
- Pilot
How high can the airplane's pilot see 0.001 of Earth's surface?
- House roof
The house's roof is a regular quadrangular pyramid with a base edge 20 m. If the roof pitch is 38° and we calculate 12% of waste, connections, and overlapping of the area roof, how much m² is needed to cover the roof?
- Observatory and aircraft
The aircraft flying towards the observatory was aimed at a distance of 5300 m at an elevation angle of 28º and after 9 seconds at a distance of 2400 m at an elevation angle of 50º. Calculate the distance the plane has flown in this time interval, its spee
- Cuboid diagonal
Calculate the volume and surface area of the cuboid ABCDEFGH, which sides a, b, and c have dimensions in the ratio of 10:8:9. If you know that the diagonal wall AC is 75 cm, and the angle between AC and space diagonal AG is 30 degrees.
- Angle of the body diagonals
Using the vector dot product calculate the angle of the body diagonals of the cube.
- Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the ball's surface and the area of the base is 4:3. A plane passing through the axis of a cone cuts the cone in an isosceles triangle
- Perpendicular forces
Distribute the force of magnitude F = 100 N into two perpendicular components with magnitudes F1 and F2 so that the angle between forces F1 and F is 43°52'.
- Tropical, mild and arctic
How many percent of the Earth's surface lies in the tropical, mild, and arctic ranges? The border between the ranges is the parallel 23°27' and 66°33'.
- Regular quadrangular pyramid
How many square meters are needed to cover the shape of a regular quadrangular pyramid base edge of 10 meters if the deviation lateral edges from the base plane are 68°? Calculate waste 10%.
- Big Earth
What percentage of the Earth's surface is seen by an astronaut from a height of h = 350 km? Take the Earth as a sphere with a radius R = 6370 km.
- Inclined plane
The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body.
- An azimuth
The patrol had started at a designated marching angle (an azimuth) of 13°. After 9 km, the azimuth's angle changed to 62°. The patrol went 10 km in this direction. Find the distance from where the patrol started.
- Vector components
The force R = 12 N is divided into two components, F1 and F2. Their directions make angles α = 30°, β = 45° with the direction R. What are the components F1 and F2?
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