# Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

1. Angle Draw angle |∠ ABC| = 130° and built its axis. What angle is between axis angle and arm of angle?
2. Triangle P2 Can triangle have two right angles?
3. Angles of the triangle ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC.
4. Seeds The field has a rectangular shape with dimensions of 128 m and 350 m. How many kg of seed are needed for sowing if the 1 m2 will consume 25 g of seeds?
5. Maple Maple peak is visible from a distance 3 m from the trunk from a height of 1.8 m at angle 62°. Determine the height of the maple.
6. Angles ratio The internal angles of a triangle are in ratio 1:4:5 What kind of triangle is it? (solve internal angles and write down and discuss)
7. Reflector Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?
8. Circles In the circle with a radius 7.5 cm are constructed two parallel chord whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions write both).
9. Pipeline How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
10. Inclined plane On the inclined plane with an angle of inclination of 30 ° we will put body (fixed point) with mass 2 kg. Determine the acceleration of the body motion on an inclined plane.
11. Garden Rectangular garden has a length 99 m and width 84 m. Calculate how many m2 will decrease its area if land by ornamental fence with width 30 cm.
12. Circles How many different circles is determined by 9 points at the plane, if 6 of them lie in a straight line?
13. Diagonal Can a rhombus have the same length diagonal and side?
14. Euclid 5 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
15. Cosine Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
16. Clouds From two points A and B on the horizontal plane was observed forehead cloud above the two points under elevation angle 73°20' and 64°40'. Points A , B are separated by 2830 m. How high is the cloud?
17. Square If we increase one side of square by its one-half then square perimeter increase by 10 cm. What is the side of the square?
18. Annulus Two concentric circles form an annulus of width 10 cm. The radius of the smaller circle is 20 cm. Calculate the content area of annulus.
19. Climb For horizontal distance 4.2 km road rise by 6.3 m. Calculate the road pitch in ‰ (permille, parts per thousand).
20. 4-gon It is true that a 4-gon whose two sides are parallel and the other two has equal length, is a parallelogram?

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