# Pythagorean theorem - problems - page 20

- Tree trunk

From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section. - Rhombus OWES

OWES is a rhombus given that OW 6cm and one diagonal measures 8cm. Find its area? - Regular n-gon

Which regular polygon have a radius of circumscribed circle r = 10 cm and the radius of inscribed circle p = 9.962 cm? - Hypotenuse

Calculate the length of the hypotenuse of a right triangle if the length of one leg is 4 cm and its content area is 16 square centimeters. - Cone

Calculate the volume of the rotating cone with a base radius 26.3 cm and a side 38.4 cm long. - Quadrangular pyramid

Calculate the surface area and volume of a regular quadrangular pyramid: sides of bases (bottom, top): a1 = 18 cm, a2 = 6cm angle α = 60 ° (Angle α is the angle between the side wall and the plane of the base.) S =? , V =? - RT perimeter

The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference. - Rectangle 35

Find the area of a rectangle when the diagonal is equal to 30 cms and the width is double the length. - Two aircraft

From the airport will start simultaneously two planes, which fly tracks are perpendicular to each other. The first flying speed of 680 km/h and the second 840 km/h. Calculate how far the aircraft will fly for half an hour. - Stairway

Stairway has 20 steps. Each step has a length of 22 cm and a height of 15 cm. Calculate the length of the handrail of staircases if on the top and bottom exceeds 10 cm. - A mast

A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken? - Plane II

A plane flew 50 km on a bearing 63degrees20 and the flew on a bearing 153degrees20 for 140km. Find the distance between the starting point and the ending point - Rectangular triangle PQR

In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decimal - Medians of isosceles triangle

The isosceles triangle has a base ABC |AB| = 16 cm and 10 cm long arm. What are the length of medians? - Diagonal of square

Calculate the side of a square when its diagonal is 10 cm. - Double ladder

The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart? - Diagonals

Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus. - Forces on earth directions

A force of 60 N [North] and 80 N [East] is exerted on an object wigth 10 kg. What is the acceleration of the object? - Ladder

The ladder has a length 3.5 meters. He is leaning against the wall so that his bottom end is 2 meters away from the wall. Determine the height of the ladder. - Hexagon area

The center of the regular hexagon is 21 cm away from its side. Calculate the hexagon side and its area.

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Pythagorean theorem is the base for the right triangle calculator.