# Triangle - math word problems

1. 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.
2. Building
How high is the building that throws horizontal shadow 95.4 m long at angle 50°?
3. Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
4. 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.
5. Equilateral triangle
How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
6. Infinity
In a square with side 18 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares.
7. Logs
Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
8. Rectangle
The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
9. 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
10. 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.
11. 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?
12. Rhombus ABCD
Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
13. Slope
What is the slope of a line with an inclination 6.06 rad?
14. IS triangle
Calculate interior angles of the isosceles triangle with base 46 cm and legs 49 cm long.
15. Rhombus
Internal angles of rhombus is in ratio 2:3. How many times is the shorter diagonal longer than side of rhombus?
16. 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?
17. 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].
18. IS trapezoid
Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
19. Regular 5-gon
Calculate area of the regular pentagon with side 7 cm.
20. Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes.

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