Practice problems of the right triangle - page 63 of 82
A right triangle is a type of triangle that has one angle that measures exactly 90 degrees (a right angle). This angle is formed by the intersection of two of the triangle's sides, which are called the legs of the triangle. The other side of the triangle is called the hypotenuse, which is the side opposite the right angle, and is the longest side of the triangle. Right triangles are important in mathematics and are used in many areas of science and engineering, including trigonometry, physics, and construction. The Pythagorean theorem which states that in a right triangle, the sum of the squares of the legs (a,b) equals the square of the hypotenuse (c) is a fundamental result in geometry.Number of problems found: 1623
- Mountain railway
The railway line's height difference between points A and B is 38.5 meters. Their horizontal distance is 3.5 km. Determine the average climb in permille up the track. - Pentagon
Calculate the length of a regular pentagon's side, circumference, and area, inscribed in a circle with a radius r = 6 cm. - Rhombus
Calculate the perimeter and area of a rhombus whose diagonals are 39 cm and 51 cm long. - On line
On line p: x = 4 + t, y = 3 + 2t, t is R, find point C, which has the same distance from points A [1,2] and B [-1,0].
- Distance of lines
Find the distance of lines AE, CG in cuboid ABCDEFGH, if given | AB | = 3cm, | AD | = 2 cm, | AE | = 4cm - Calculate 5789
Calculate the volume and surface of the rotating cone with the base radius r = 4.6dm and the height v = 230mm. - 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. - The mast
A 40 m high mast is secured in half by eight ropes 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance. - Six-sided 44151
The parasol has the shape of the shell of a regular six-sided pyramid, whose base edge is a=6dm and height v=25cm. How much fabric is needed to make a parasol if we count 10% for joints and waste?
- Calculate 82578
The vertices of triangle ABC are: A[1, 2, -3], B[0, 1, 2], C[2, 1, 1]. Calculate the lengths of sides AB, AC and the angle at vertex A. - Quadrilateral oblique prism
What is the volume of a quadrilateral oblique prism with base edges of length a = 1m, b = 1.1m, c = 1.2m, d = 0.7m if a side edge of length h = 3.9m has a deviation from the base of 20° 35' and the edges a, b form an angle of 50.5°? - Rectangle
In a rectangle with sides, 8 and 9 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than any side of the rectangle? - Earth's circumference
Calculate the Earth's circumference of the parallel 48 degrees and 10 minutes. - Octagonal tank
The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, and the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness.
- Sphere equation
Obtain the equation of a sphere. Its center is on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Calculate 30971
Calculate the cone's surface and volume if its base diameter is 1 dm and the side length is 13 cm. - Cone - from volume surface area
The volume of the rotating cone is 1,018.87 dm3, and its height is 120 cm. What is the surface area of the cone? - Parallelogram 82626
Calculate the area of a parallelogram if we know the perimeter is 23 cm, the diagonal is 8.5 cm, and one side is 1.5 cm longer. - Cross-section 46841
The cross-section of the channel has the shape of a trapezoid. The bottom width is 2.25 m, and the depth is 5 m. The walls have a slope of 68°12' and 73°45'. Calculate the upper channel width.
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