# Pythagorean theorem - problems - page 3

- Prism

Right angle prism, whose base is right triangle with leg a = 7 cm and hypotenuse c = 15 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube - 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. - Cone

Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°. - Spherical cap

From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere? - Right triangle

Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle. - Railways

Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters. - Rhombus

It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 14 cm and a_{2}= 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Rectangle

Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees. - Isosceles right triangle

Calculate the area of an isosceles right triangle whose perimeter is 377 cm. - R triangle

Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg. - Rhombus and inscribed

Rhombus has side a = 42 cm, the radius of the inscribed circle is r = 18 cm. Calculate the length of its two diagonals. - Laws

From which law follows directly the validity of Pythagoras' theorem in the right triangle? ? - Medians

Calculate the sides of a right triangle if the length of the medians to the legs are t_{a}= 21 cm and t_{b}=12 cm. - Rectangle SS

Perimeter of a rectangle is 296 km and its diagonal is 104.74 km. Determine the dimensions of the rectangle. - Diagonal

Determine the dimensions of the cuboid, if diagonal long 31 dm has angle with one edge 61° and with other edge 52°. - Infinity

In a square with side 8 is inscribed circle, in circle is inscribed next square, again circle and so on to infinity. Calculate the sum of area of all these squares. - 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. - Triangle

Can be rectangular triangle equilateral? - R Trapezium

Rectangular trapezium has bases 18 and 11 and area 28 cm^{2.}What is its perimeter? - Ladder

Ladder 8 m long is leaning against the wall. It foot is 1 m away from the wall. In which height ladder touch the wall?

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Pythagorean theorem is the base for the right triangle calculator.