Planimetrics - high school - practice problems - page 51 of 52
Number of problems found: 1032
- Vectors
Find the magnitude of the angle between two vectors u = (3; -5) and v = (10; 6) - Vector sum
The magnitude of the vector u is 12 and the magnitude of the vector v is 8. The angle between vectors is 61°. What is the magnitude of the vector u + v? - Subtended 83194
A circle k with a center at point S and a radius of 6 cm is given. Calculate the size of the central angle subtended by a chord 10 cm long. - Fighter
A military fighter flies at an altitude of 10 km. The ground position was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
- Inclination 34381
A skier starts down a hill of length l and an angle of inclination of 10˚. It then moves to a horizontal section of the track, which travels the same length l until it stops. Determine the coefficient of sliding friction between the skis and the snow. - Angle in RT
Determine the size of the smallest internal angle of a right triangle whose sides constitute the sizes of consecutive members of arithmetic progressions. - Triangle KLB
It is given 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 percents of the area of the triangle ABC - Raindrops
The train is moving at a speed of 60 km/h. Raindrops falling vertically in the absence of wind (with uniform movement due to the action of air resistance) leave traces on the windows of the train, deviating from the vertical direction by 30°. How fast are - Toboggan 5710
The length of the toboggan run is 60 m, and the height is 8 m. The boy pulls a sled weighing 15 kg. How hard does the boy pull the sled uphill?
- Ball
The soldier fired the Ball at an angle of 35° at an initial velocity of 292 m/s. Determine the length of the litter. (g = 9.81 m/s²). - Observatory 71934
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 - 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. - Three vectors
The three forces whose amplitudes are in ratio 9:10:17 act in the plane at one point to balance. Determine the angles of each two forces. - Coefficient 82566
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? - 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. - 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 - Isosceles 83157
Using the cosine theorem, prove that in an isosceles triangle ABC with base AB, c=2a cos α. - Perpendicular 7005
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
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