Right triangle - examples - page 12

1. Center of the cube
Center of the cube has distance 33 cm from each vertex. Calculate the volume V and surface area S of the cube.
2. Triangle
Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
3. Unit vector 2D
Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
4. Complete construction
Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
5. Isosceles triangle
What are the angles of an isosceles triangle ABC if its base is long a=5 m and has an arm b=4 m.
6. Cube - wall
V kocke ABCDEFGH je ?. Aký je povrch kocky?
7. RT 11
Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
8. IS trapezoid
Isosceles trapezoid arm measured 35 cm. Height is 30 cm and middle segment is 65 cm. Determine length of its bases.
9. Diamond ABCD
In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond.
10. Estate
Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence.
11. Square pyramid
Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
12. Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
13. Moon
We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
14. Mountain railway
Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
15. Height 2
Calculate the height of the equilateral triangle with side 38.
16. Sphere cuts
At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.
17. 30-60-90
The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg?
18. Spherical cap
What is the surface area of a spherical cap, the base diameter 20 m, height 2 m.
19. Building
The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
20. RT and ratio
A right triangle whose legs are in a ratio 6:12 has hypotenuse 68 m long. How long are its legs?

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