Practice problems of the triangle - page 49 of 117
A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. The sum of the measures of the interior angles of a triangle is always 180 degrees. An exterior angle of a triangle is an angle that is a linear pair (and hence supplementary) to an interior angle. The best known area formula is T = a*h /2 where a is the length of the side of the triangle, and h is the height or altitude of the triangle.Number of problems found: 2329
- Rotary cone
The volume of the rotation of the cone is 472 cm³. The angle between the side of the cone and the base angle is 70°. Calculate the lateral surface area of this cone. - Railways
Railways climb 2.8 ‰. Calculate the height difference between two points on the railway distant 5997 meters. - Determine 67754
Adam (A) stands on one river bank, and Bedrich (B) stands on the other. To determine their distance, the base AC with a length of 136 m and the angles CAB with a size of 70°21' and ACB with a size of 43°44' were measured on one river bank. What is the dis - 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. - Triangular prism
Calculate the surface of a triangular prism with the base of an equilateral triangle with a side length of 7.5 cm and a corresponding height of 6.5 cm. Prism height is 15cm. - 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. - Centimeters 80859
Triangle ABC and triangle ADE are similar. Calculate in square centimeters the area of triangle ABC if the length of side DE is 12 cm, the length of side BC is 16 cm, and the area of triangle ADE is 27 cm². - Equilateral 82136
A three-sided prism with a base in the shape of an equilateral triangle has a volume of 370 dm³. What is the volume of its base if it is 50 cm high? - 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. - Triangle 67504
Sestroj triangle HOP, if o = 6 cm, h = 8 cm and | PHO | = 90 °
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