# Right triangle - problems - page 20

1. Diagonal - simple
Calculate the length of the diagonal of a rectangle with dimensions 5 cm and 12 cm.
2. Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm.
Show that the quadrilateral with vertices P1(0,1), P2(4,2) P3(3,6) P4(-5,4) has two right triangles.
4. Railway
Between points A, B, whose horizontal distance is 1.5 km railway line has 8promile climb. Between points B, C with horizontal distance of 900 m is climb 14promile. Calculate differences of altitudes between points A and C.
5. Right angled triangle
Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs.
6. Broken tree
The tree was 35 meters high. The tree broke at a height of 10 m above the ground. Top but does not fall off it refuted on the ground. How far from the base of the tree lay its peak?
7. Cube
Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
8. Drainage channel
The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel.
9. Bearing
A plane flew 50 km on a bearing 63°20' and the flew on a bearing 153°20' for 140km. Find the distance between the starting point and the ending point.
10. Ethernet cez ulicu
Karol a Jozef sú vášniví hráči počítačových hier a býva v domoch, ktoré sú presne naproti sebe cez ulicu, takže si vidia navzájom do okien. Rozhodli sa, že si svoje počítače prepoja telefónnym káblom aby mohli hrať spoločne hry. Karol býva v prvom poschodí
11. Medians and sides
Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
12. Triangle KLM
In the rectangular triangle KLM, where is hypotenuse m (sketch it!) find the length of the leg k and the height of triangle h if hypotenuse's segments are known mk = 5cm and ml = 15cm
13. Rectangle 3-4-5
The sides of the rectangle are in a ratio of 3:4. The length of the rectangle diagonal is 20 cm. Calculate the content of the rectangle.
14. Triangle ABC v2
Area of the triangle is 12 cm square. Angle ACB = 30º , AC = (x + 2) cm, BC = x cm. Calculate the value of x.
15. The mast
A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
16. Angle
Determine the size of the smallest internal angle of a right triangle which angles forming the successive members of the arithmetic sequence.
17. Medians and sides
Triangle ABC in the plane Oxy; are the coordinates of the points: A = 2.7 B = -4.3 C-6-1 Try calculate lengths of all medians and all sides.
18. V-belt
Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
19. Right triangles
How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality).