Practice problems of the triangle - page 27 of 116
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: 2311
- Poplar shadow
The nine-meter poplar casts a shadow 16.2 m long. How long does a shadow cast by Peter at the same time if it is 1.4 m high? - Similar triangles
The triangles ABC and XYZ are similar. Find the missing lengths of the sides of the triangles. a) a = 5 cm b = 8 cm x = 7.5 cm z = 9 cm b) a = 9 cm c = 12 cm y = 10 cm z = 8 cm c) b = 4 cm c = 8 cm x = 4.5 cm z = 6 cm - Mast shadow
The mast has a 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at an angle of 15°. Determine the height of the mast if the sun above the horizon is at an angle of 33°. Use the law of sines. - Determine 70834
At the same time, a vertical 2-meter pole casts a shadow of 0.85 meters. At the same time, a chimney of unknown height casts a 45m long shadow. Determine the height of the chimney. - Vertical 29801
The shadow of the building is 16 m long, and the shadow of the vertical meter rod is 0.8 m long at the same time. What is the height of the building? - Construct 4129
Construct a triangle ABC, given the lengths of the sides c = 8 cm, a = 5 cm and length length Vc = 3.5 cm. Perform an analysis, write down the design procedure, perform it, and determine the number of solutions. - Shadows
At the park, a young woman who is 1.72 meters tall casts a 3.5 meters shadow at a certain hour. What is the height of a tree in the park that, at the same time, casts a 12.3 meters shadow? - A boy
A boy of height 1.7m is standing 30m away from the flagstaff on the same level ground. He observes that the angle of deviation of the top of the flagstaff is 30 degrees. Calculate the height of the flagstaff. - Triangle SSA
Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps. - Boat
A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weigh? - Construction 83208
An isosceles triangle ABY with a base AB of length 5 cm and an angle at the main vertex of 50°. Write down the construction progress. - Equilateral 35073
Draw an equilateral triangle ABC with a side of 8.5 cm. Assemble all the mines and measure them. What is the difference between the longest and the shortest of them? - RST triangle
Find out if it is possible to construct the given triangle and according to which theorem: RS = 2.5 cm ST = 7 cm TR = 4.5 cm - Inclined plane
On the inclined plane with an inclination angle of 30°, we will put the body (fixed point) with mass 9 kg. Determine the acceleration of the body motion on an inclined plane. - Calculate 82282
Calculate the sizes of the interior angles in the triangle whose vertices are the points marked by the numbers 1, 5, and 8 on the clock face. - Two-meter 3473
A tree with an unknown height casts a shadow 18 m long at a time, while a two-meter pole casts a shadow of 2.4 m. How tall is the tree? - Construction
Construct the triangle ABC if you know: the size of the side AC is 6 cm, the size of the angle ACB is 60°, and the distance of the center of gravity T from the vertex A is 4 cm. (Sketch, analysis, notation of construction, construction) - Similar triangles
Triangle A'B'C 'is similar to triangle ABC, whose sides are 5 cm, 8 cm, and 7 cm long. What is the length of the sides of the triangle A'B'C' if its circumference is 80 cm? - The shadow
The shadow of a 1 m high pole thrown on a horizontal plane is 0.8 m long. At the same time, the shadow of a tree thrown on a horizontal plane is 6.4 m. Determine the height of the tree. - Coordinates 32183
The triangle ABC is given in the plane. A (-3,5), B (2,3), C (-1, -2) write the coordinates of the vectors u, v, w if u = AB, v = AC, and w = BC. Enter the coordinates of the centers of the lines SAB (..), SAC (...), SBC (. ..)
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