# Right triangle - math word problems

1. The garden
The garden has the shape of a rectangular trapezium. The bases have lengths of 27 meters and 36 meters, the trapezoid's height is 12 meters. Calculate how much fence will cost this garden if one meter costs 1.5 €?
2. The mast
The top of the pole we see at an angle of 45°. If we approach the pole by 10 m, we see the top of the pole at an angle of 60°. What is the height of the pole?
3. Three points
Three points A (-3;-5) B (9;-10) and C (2;k) . AB=AC What is value of k?
4. On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
5. Center of line segment
Calculate the distance of the point X [1,3] from the center of the line segment x = 2-6t, y = 1-4t ; t is .
6. Distance problem 2
A=(x,2x) B=(2x,1) Distance AB=√2, find value of x
7. Distance problem
A=(x, x) B=(1,4) Distance AB=√5, find x;
8. Cube diagonals
The cube has a wall area of 81 cm square. Calculate the length of its edge, wall, and body diagonal.
9. Square
Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
10. AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
11. Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
12. Pavement
Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.
13. The swimmer
The swimmer swims at a constant speed of 0.85 m/s relative to water flow. The current speed in the river is 0.40 m/s, the river width is 90 m. a) What is the resulting speed of the swimmer with respect to the tree on the riverbank when the swimmer motio
14. Paratrooper
After the parachute is opened, the paratrooper drops to the ground at a constant speed of 2 m/s, with the sidewinding at a steady speed of 1.5 m/s. Find: a) the magnitude of its resulting velocity with respect to the ground, b) the distance of his land f
15. Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
16. Circle annulus
There are 2 concentric circles in the figure. Chord of larger circle 10 cm long is tangent to the smaller circle. What are does annulus have?
17. Bricklayer
How much do we pay for a bricklayer laying a pavement in a square room with a diagonal of 8 m, if 1 sqm with work will cost for CZK 420?
18. Equilateral triangle ABC
In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont
19. Perpendicular prism
Calculate the volume of the perpendicular prism if its height is 60.8 cm and the base is a rectangular triangle with 40.4 cm and 43 cm legs.