# Right triangle + expression of a variable from formula - problems

1. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
2. Find parameters
Find parameters of the circle in the plane - coordinates of center and radius: ?
3. Spherical cap 4
What is the surface area of a spherical cap, the base diameter 20 m, height 2.5 m? Calculate using formula.
4. Pile of sand
A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
5. Cincinnati
A map is placed on a coordinate grid. Cincinnati located at (5,4) and San Diego is located at (-10, -3). How far apart is Cincinnati from San Diego on the map? Round to the nearest tenth.
6. Spherical cap
Place a part of the sphere on a 4.6 cm cylinder so that the surface of this section is 20 cm2. Determine the radius r of the sphere from which the spherical cap was cut.
7. Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.
8. Balloon and bridge
From the balloon, which is 92 m above the bridge, one end of the bridge is seen at a depth angle of 37° and the second end at depth angle 30° 30 '. Calculate the length of the bridge.
9. Right Δ
Right triangle has length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
10. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
11. Square diagonal
Calculate length of the square diagonal if the perimeter is 476 cm.
12. 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.
13. Floating barrel
Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
14. R Trapezium
Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
15. ISO triangle
Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
16. Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
17. Right isosceles
Calculate area of the isosceles right triangle which perimeter is 41 cm.
18. Square diagonal
Calculate the length of diagonal of the square with side a = 23 cm.
19. Right triangle
Calculate the missing side b and interior angles, perimeter and area of ​​a right triangle if a=10 cm and hypotenuse c = 16 cm.
20. Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg and its content area is 24 cm2.

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