# Triangle - math word problems

1. Triangle For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle?
2. Tetrahedral pyramid What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16?
3. Side c In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
4. 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.
5. Stairway What angle rising stairway if step height in 17 cm and width 27 cm?
6. Distance Calculate distance between two points X[18; 19] and W[20; 3].
7. Observer The observer sees straight fence 100 m long in 30° view angle. From one end of the fence is 153 m. How far is it from the another end of the fence?
8. 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.
9. Triangle ABC Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
10. 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.
11. Equilateral triangle How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
12. Recursion squares In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of al
13. Rectangle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
14. Triangle in circle Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
15. Garden Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden?
16. Rhombus ABCD Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
17. IS triangle Calculate interior angles of the isosceles triangle with base 46 cm and legs 49 cm long.
18. Rhombus Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus?
19. Short cut Imagine that you are going to the friend. That path has a length 120 meters. Then turn doprava and go another 630 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
20. Center In the triangle ABC is point D[1,-2,6], which is the center of the |BC| and point G[8,1,-3], which is the center of gravity of the triangle. Find the coordinates of the vertex A[x,y,z].

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