# Pythagorean theorem - problems - page 5

- Without Euclid laws

Right triangle ABC with right angle at the C has a=10 and hypotenuse c=27. Calculate the height h of this triangle without the use of Euclidean laws. - Square diagonal

Calculate the length of diagonal of the square with side a = 18 cm. - Crossroads

The rectangular crossroads comes passenger car and an ambulance, the ambulance left. Passenger car is at 45 km/h and ambulance 58 km/h. Calculate such a relative speed of the ambulance moves to the car. - Road embankment

Road embankment has a cross section shape of an isosceles trapezoid with bases 9 m and 12 m, and 4 m long leg. How many cubic meters of soil is in embankment length of 758 meters? - 4side pyramid

Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees. - Canopy

Mr Peter has metal roof cone shape with a height of 36 cm and radius 73 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 2.1 m^{2}? - Square 2

Points D[9,-1] and B[3,3] are opposed vertices of the square ABCD. Calculate area of the square ABCD. - Pyramid a+h

Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm. - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 14 cm and central angle 114 degrees. - Circle section

Equilateral triangle with side 50 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector. - Square

Calculate area of the square with diagonal 70 cm. - 4s pyramid

Regular tetrahedral pyramid has a base edge a=6 and collaterally edge length b=15. What is its height? - Tetrahedral pyramid

Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm^{2}and deviation angle of the side edges from the plane of the base is 60 degrees. - Angle between vectors

Find the angle between the given vectors to the nearest tenth of a degree. u = (24, -1) and v = (12, 16) - Height

Is right that in any right triangle height is less or equal half of the hypotenuse? - Circle

Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: -x+3y+1 = 0 q: x-3y-1 = 0 a: -10x-3y-2 = 0 - Triangular pyramid

Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm. - Track arc

Two straight tracks is in an angle 99°. They will join with circular arc with radius r=1292 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)? - Arm

Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 16 cm and a height v=10 cm. - Prism

The lenght, width and height of a right prism are 18, 14 and 9 respectively. What is the lenght of the longest segment whose endpoints are vertices of the prism?

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Pythagorean theorem is the base for the right triangle calculator.