Pythagorean theorem - high school - practice problems - page 9 of 30
Number of problems found: 600
- Equation of the circle
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3], and C[9, 4]. - Ratio of squares
A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the square's side and the circle's arc. What is the ratio of the areas of the large and small squares? - Triangular prism
The triangular prism has a base in the shape of a right triangle, the legs of which are 9 cm and 40 cm long. The height of the prism is 20 cm. What is its volume cm³? And the surface cm²? - Rotating 28501
Which bags shaped like the shell of a rotating cone can hold the most popcorn? The first bag has a height of 20 cm, and the length of its side is 24 cm. The second bag has a base radius of 10 cm and a height of 25 cm. - Calculate 6
Calculate the distance of point A[0, 2] from a line passing through points B[9, 5] and C[1, -1]. - 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. - Rotating 28001
There is a rotating cone: r = 6.8 cm s = 14.4 cm. Find the area of the cone surface S2, the height h, and the volume V. - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Isosceles 27793
The LICH isosceles trapezoid has 5.2 cm long arms and its bases are 7.6 cm and 3.6 cm long. Find the area of the LICH trapezoid. - Hexagonal pyramid
Find the volume of a regular hexagonal pyramid, the base edge 12 cm long and the side edge 20 cm. - 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]. - 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? - Motorcyclist 26141
The passenger car left at 7:00 and was heading east at a speed of 60km/h. A motorcyclist left the same place and headed north at 40 km/h. What will be their air distance at ten o'clock? - Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long. - Triangle in a square
In a square ABCD with side a = 6 cm, point E is the center of side AB, and point F is the center of side BC. Calculate the size of all angles of the triangle DEF and the lengths of its sides. - 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). - The right triangle
In the right triangle ABC with a right angle at C, we know the side lengths AC = 9 cm and BC = 7 cm. Calculate the length of the remaining side of the triangle and the size of all angles. - Isosceles triangle
Calculate the size of the interior angles and the length of the base of the isosceles triangle if the arm's length is 17 cm and the height of the base is 12 cm.
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