Expression of a variable from the formula + Pythagorean theorem - practice problems - page 11 of 29
Number of problems found: 578
- Right triangle - ratio
The lengths of the legs of the right triangle ABC are in ratio b = 2:3. The hypotenuse is 10 cm long. Calculate the lengths of the legs of that triangle. - Traffic sign
There is a traffic sign for climbing on the road with an angle of 7%. Calculate at what angle the road rises (falls). - Height of pyramid
The pyramid ABCDV has edge lengths: AB = 4, AV = 7. What is its height? - Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD.
- The tent
The tent has the shape of a regular square pyramid. The edge of the base is 3 m long, and the tent's height is 2 m. Calculate how much cover (without a floor) is used to make a tent. - Millimeter 24231
Calculate the length of the wall diagonal of a cube with a volume of 7.40 square meters. Express the result to the nearest millimeter. - Quadrilateral 24161
Calculate the volume of a quadrilateral prism whose base is an isosceles trapezoid with bases 10 cm and 4 cm, 6 cm apart. The height of the prism is 25 cm. How could the surface area be calculated? - Triangular 24091
A regular triangular prism with a base edge of 35 cm has a volume of 22.28 l. Calculate the height of the prism. - Quadrilateral pyramid
Calculate the surface of a quadrilateral pyramid, which has a rectangular base with dimensions a = 8 cm, b = 6 cm, and height H = 10 cm.
- Administrator 23801
The administrator of the castle is trying to estimate how many square meters of sheet metal will be needed for the new roof of the tower. The roof has the shape of a cone. The castle administrator knows that the tower's diameter is 4.6 meters and its heig - Quadrilateral 23701
We know the base diagonal length of u = 4 cm in a regular quadrilateral pyramid. The height of the pyramid is v = 5cm. Calculate the size of the side edge and the base edge of the pyramid. - Cross-section 23491
The cross-section of the railway embankment is an isosceles trapezoid, the bases of which are in a ratio of 5:3. The arms have a 5 m embankment height v = 4.8 m. Calculate the section area S. - The right triangle
The right triangle ABC has a leg a = 36 cm and an area S = 540 cm². Calculate the length of the leg b and the median t2 to side b. - Concentric circles and chord
In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius has the concentric circle while touching this chord?
- Spherical cap
The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut. - Quadrilateral 21523
Calculate the surface area and volume of a regular quadrilateral pyramid if the edge of the lower base is 18 cm and the edge of the upper base is 15 cm. The wall height is 9 cm. - A kite
Children have a kite on an 80m long rope, which floats above a place 25m from the place where children stand. How high is the dragon floating above the terrain? - Difference of legs
In a right triangle, the hypotenuse length is 65 m, and the difference between legs is 23 m. Calculate the perimeter of this triangle. - Base of an isosceles triangle
Calculate the size of the base of an isosceles triangle, the height is 5 cm, and the arm's length is 6.5 cm. What is the perimeter of this triangle?
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