Pythagorean theorem - problems - page 6
- Rotating cone II
Calculate area of surface of rotating cone with base radius r=7 cm and height h=17 cm.
Calculate the length of the belt on pulleys with diameters of 162 mm and 454 mm at shaft distance 425 mm.
- 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.
- 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.
- Two forces
Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
- EQL triangle
Calculate inradius and circumradius of equilateral triangle with side a=100 cm.
If tg α = 3.8, Calculating sin α, cos α, cotg α .
- Equilateral triangle
Calculate the side of an equilateral triangle, if its area is 79 mm2.
- Airplane navigation
An airplane leaves an airport and flies due west 120 miles and then 150 miles in the direction S 23.32°W. How far is the plane from the airport (round to the nearest mile)?
- Cone and the ratio
Rotational cone has a height 28 cm and the ratio of the base surface to lateral surface is 4: 7. Calculate a surface of the base and the lateral surface.
Legs of a right triangle have dimensions 61 m and 39 m. Calculate the length of the hypotenuse and the height of this right triangle.
Calculate length of the vector v⃗ = (-2.5, 6.25, -4.25).
- Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
- Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.
How far can you see from the ship's mast, whose peak is at 11 meters above sea level? (Earth's radius is 6370 km).
- Triangle and its heights
Calculate the length of the sides of the triangle ABC, if va=13 cm, vb=17 cm and side b is 5 cm shorter than side a.
What must be the elevation of an observer in order that he may be able to see an object on the earth 814 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
Pit has shape of a truncated pyramid with rectangular bases and is 2.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.3 l of green colour. How many liters of paint is needed when w
- Sphere and cone
Within the sphere of radius G = 26 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
In right triangle ABC with right angle at C is given side a=29 and height v=27. Calculate the perimeter of the triangle.
Pythagorean theorem is the base for the right triangle calculator.