Practice problems of the right triangle - page 31 of 81
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: 1619
- The chimney
How high is the chimney if we see it from a distance of 60 m at an angle of 42°? - Map - climb
On the map of the High Tatras, on a scale of 1:11000, are cable car stations in the Tatranska Lomnica and the Skalnate Pleso with a distance of 354.6 mm. The altitude of these stations is 949 m and 1760 m. What is the average angle of climb on this cable - Isosceles + prism
Calculate the volume of the perpendicular prism if its height is 17.5 cm and the base is an isosceles triangle with a base length of 5.8 cm and an arm's length of 3.7 cm - Rotating cone
Find the rotating cone's surface and volume if its side is 150 mm long and the circumference of the base is 43.96 cm. - Lateral surface area
The ratio of the area of the base of the rotary cone to its lateral surface area is 3:5. Calculate the surface and volume of the cone if its height v = 4 cm. - Cube diagonals
Determine the volume and surface area of the cube if you know the length of the body diagonal u = 216 cm. - Rotation of the Earth
Calculate the circumferential speed of the Earth's surface at a latitude of 61°. Consider a globe with a radius of 6378 km. - Decimetres 4163
Determine the length of the body and wall diagonals of the cube, the volume of which is equal to 0.343 decimetres. Also, calculate its surface. - Lengths of medians from coordinates
There is a triangle ABC: A [-6.6; 1.2], B [3.4; -5.6], C [2.8; 4.2]. Calculate the lengths of its medians. - Calculate 30961
Calculate the cone's surface and volume if its base diameter is 12 cm and the height is 150 mm. - Increased 20383
We threw a prism with the base of a right triangle with squares 15 × 10 cm and a prism height of 1.5 dm into a 10 l bucket. How much has the volume in the bucket increased? - Calculate 3019
The height is 5 cm, and the size of the angle that the side of the cone with the base makes is 63 degrees. Calculate the surface and volume of this cone. - Nice prism
Calculate the cuboid's surface if the sum of its edges is a + b + c = 19 cm and the body diagonal size u = 13 cm. - Cone and the ratio
The rotational cone has a height of 43 cm, and the ratio of the base surface to the lateral surface is 5: 7. Calculate the surface of the base and the lateral surface. - Triangle 67504
Sestroj triangle HOP, if o = 6 cm, h = 8 cm and | PHO | = 90 ° - Ratio of triangles areas
In an equilateral triangle ABC, the point T is its center of gravity, the point R is the image of the point T in axial symmetry along the line AB, and the point N is the image of the point T in axial symmetry along the line BC. Find the ratio of the areas - Right triangles
How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget the triangle inequality). - Identical 35961
Nine identical spheres are stacked in the cube to fill the volume of the cube as much as possible. What part of the volume will the cube fill? - Perpendicular 35183
Calculate the surface and volume of a vertical prism if its height h = 18 cm and if the base is an equilateral triangle with side length a = 7.5 cm. - 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.
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