Equation + triangle - practice problems - page 6 of 15
Number of problems found: 289
- An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - Two groves
Two groves A B are separated by a forest. Both are visible from the hunting grove C, which is connected to both by direct roads. What will be the length of the projected road from A to B if AC = 5004 m, BC = 2600 m, and angle ABC = 53° 45'? - Branches 18533
The right triangle has an area of 225 cm². One of its branches is twice the size of the other. Find the lengths of its hangers. - Angled cyclist turn
The cyclist passes through a curve with a radius of 20 m at 25 km/h. How much angle does it have to bend from the vertical inward to the turn?
- Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle? - There
There is a stretched steel cable between the three columns. The height of the first column is 4 m, and the height of the second is 3.5 m. The distance between the first two columns is 2.5 m, and the distance between the second and third is 5 m. The heels - Parametric form
Calculate the distance of point A [2,1] from the line p: X = -1 + 3 t Y = 5-4 t Line p has a parametric form of the line equation. - One-quarter 13953
Calculate the magnitude of the interior angles of the triangle ABC if alpha = two-fifths beta and alpha = one-quarter gamma. - Three parallels
The vertices of an equilateral triangle lie on three different parallel lines. The middle line is 5 m and 3 m distant from the end lines. Calculate the height of this triangle.
- Land boundary
The land is a right triangle. Its hypotenuse is 30 meters long, and its circumference is 72 meters. What are the sizes of the remaining sides of the land boundary? - A rectangle 2
A rectangle has a diagonal length of 74cm. Its side lengths are in a ratio of 5:3. Find its side lengths. - Sides of right angled triangle
One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - 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? - Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure.
- Medians in right triangle
It is given a right triangle, and angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. How to calculate the length of the sides? - Faces diagonals
If a cuboid's diagonals are x, y, and z (wall diagonals or three faces), find the cuboid volume. Solve for x=1.3, y=1, z=1.2 - Two chords
Calculate the length of chord AB and perpendicular chord BC to the circle if AB is 4 cm from the circle's center and BC 8 cm from the center. - Circumference 9811
Kristýna chose a certain odd natural number divisible by three. Jakub and David then examined triangles with a circumference in millimeters equal to the number selected by Kristýna and whose sides have lengths in millimeters expressed by different integer - Calculate 9701
In the triangle, the side length AB = 6 cm, the height per side c = 5 cm, and the angle BCA = 35°. Calculate sides a b.
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