# Pythagorean theorem - math word problems

#### Number of problems found: 704

• An observer An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower?
• Touch x-axis Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
• Pyramid 8 Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
• Vector 7 Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
• Cone container Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package. 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 =?
• Calculate 8 Calculate the coordinates of point B axially symmetrical with point A[-1, -3] along a straight line p : x + y - 2 = 0.
• 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.
• Hexagonal pyramid Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm.
• Medians and sides Determine the size of a triangle KLM and the size of the medians in the triangle. K=(-5; -6), L=(7; -2), M=(5; 6).
• Five-gon Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.
• The regular The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
• Sailboat The 20 m long sailboat has an 8 m high mast in the middle of the deck. The top of the mast is fixed to the bow and stern with a steel cable. Determine how much cable is needed to secure the mast and what angle the cable will make with the ship's deck.
• Triangular prism The triangular prism has a base in the shape of a right triangle, the legs of which is 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm3? And the surface cm2?
• A concrete pedestal A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal.
• 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
• Rotary bodies The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
• Truncated cone 6 Calculate the volume of the truncated cone whose bases consist of an inscribed circle and a circle circumscribed to the opposite sides of the cube with the edge length a=1.
• The hemisphere The hemisphere container is filled with water. What is the radius of the container when 10 liters of water pour from it when tilted 30 degrees?
• On a line On a line p : 3 x - 4 y - 3 = 0, determine the point C equidistant from points A[4, 4] and B[7, 1].

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Pythagorean theorem is the base for the right triangle calculator.