# 8th grade (13y) + Pythagorean theorem - math problems

- Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - The ladder

The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach? - Company logo

The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo? - Garden

Area of a square garden is 6/4 of triangle garden with sides 56 m, 35 m, and 35 m. How many meters of fencing need to fence a square garden? - Right Δ

A right triangle has the length of one leg 7 cm and length of the hypotenuse 25 cm. Calculate the height of the triangle. - Cube in a sphere

The cube is inscribed in a sphere with volume 9067 cm^{3}. Determine the length of the edges of a cube. - Axial section

Axial section of the cone is an equilateral triangle with area 208 dm^{2}. Calculate the volume of the cone. - Circle chord

What is the length d of the chord circle of diameter 50 dm, if the distance from the center circle is 21 dm? - Rectangle

The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle. - Tetrahedral pyramid

What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=16 and height v=16? - Triangle SAS

Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °. - Movement

From the crossing of two perpendicular roads started two cyclists (each at different road). One runs at average speed 28 km/h, the second at average speed 24 km/h. Determine the distance between them after 45 minutes cycling. - Square

Points A[-2,5] and B[-6,7] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD. - Cubes

One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm^{2}. - Is right?

Is triangle with sides 51, 56 and 77 right triangle? - Cone A2V

Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm^{2}. Calculate the volume of a cone. - Rhombus

Calculate the perimeter and area of a rhombus whose diagonals are 38 cm and 55 cm long. - Short cut

Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field? - Gimli Glider

Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes to plane from engine failure to hit the ground. Ca - River

From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.

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Pythagorean theorem is the base for the right triangle calculator.