# 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. R Trapezium Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
2. Center Calculate the coordinates of the circle center: ?
3. Circle Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
4. Aircraft The plane flies at altitude 6500 m. At the time of first measurement was to see the elevation angle of 21° and second measurement of the elevation angle of 46°. Calculate the distance the plane flew between the two measurements.
5. 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?
6. It is rectangular? Size of two of the angles in a triangle are: α=110°, β=40°. Is it a right triangle?
7. Triangle For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle?
8. Parallelogram Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
9. Two boats Two boats are located from a height of 150m above the surface of the lake at depth angles of 57° and 39°. Find the distance of both boats if the sighting device and both ships are in a plane perpendicular to the surface of the lake.
10. Side c In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
11. Stairway What angle rising stairway if step height in 17 cm and width 27 cm?
12. Distance Calculate distance between two points X[18; 19] and W[20; 3].
13. Count of triangles Given a square ABCD and on each side 8 internal points. Determine the number of triangles with vertices at these points.
14. Observer The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 102 m. How far is it from the another end of the fence?
15. Triangle and its heights Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
16. Circle Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
17. Quarter circular The wire that is hooked around the perimeter of quarter-circular arc has length 3π+12. Determine the radius of circle arc.
18. Building How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
19. Triangle ABC Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
20. River From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.

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