Equation + triangle - practice problems - page 5 of 15
Number of problems found: 289
- Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum? - Isosceles triangle
In an isosceles triangle ABC with base AB; A [3,4]; B [1,6] and the vertex C lies on the line 5x - 6y - 16 = 0. Calculate the coordinates of vertex C. - Vertical rod
The vertical one-meter-long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long simultaneously. - 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].
- Perimeter and diagonal
The perimeter of the rectangle is 82 m, and the length of its diagonal is 29 m. Find the dimensions of the rectangle. - Integer sides
A right triangle with an integer length of two sides has one leg √11 long. How much is its longest side? - Right-angled 27683
Right-angled triangle XYZ is similar to triangle ABC, which has a right angle at the vertex X. The following applies a = 9 cm, x=4 cm, x =v-4 (v = height of triangle ABC). Calculate the missing side lengths of both triangles. - Two chords
From the point on the circle with a diameter of 8 cm, two identical chords are led, which form an angle of 60°. Calculate the length of these chords. - Regular hexagonal prism
Calculate the volume of a regular hexagonal prism whose body diagonals are 24cm and 25cm long.
- 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. - Approximately 25381
The observer sees the tops of two trees at the same angle a. It is 9 m from one tree and 21 m from the other. The trees stand on a level. How tall is the second tree if the height of the first is 6 m? Remember that the eyes of a standing person are approx - Parallelogram 25371
A parallelogram with a side length of 5 cm and a height to this side length of 4 cm has the same area as an isosceles triangle with a base length of 5 cm. What is the height of this triangle? - 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. - Magnitudes 24271
In the ABC triangle, the magnitude of the inner angle beta is one-third the magnitude of the angle alpha and 20 ° larger than the magnitude of the gamma angle. Determine the magnitudes of the interior angles of this triangle.
- Viewing angle
The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure? - Side lengths
In the triangle ABC, the height to side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b. - Interior angles
Calculate the interior angles of a triangle that are in the ratio 2:3:4. - Magnitude 23271
In an isosceles triangle, the angle at the primary vertex is 20 ° smaller than twice the magnitude of the angle at the base. What are the interior angles of a triangle? - In a
In a triangle, the aspect ratio a: c is 3: 2, and a: b is 5: 4. The perimeter of the triangle is 74cm. Calculate the lengths of the individual sides.
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