Planimetry - math word problems - page 58 of 72
Number of problems found: 1438
- 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? - Chimney shadow height
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 45 m long shadow. Determine the height of the chimney. - 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) - Triangle from sticks
Bob the boulder has many sticks of lengths 3.5 and 7. He wants to form triangles, each of whose edges consists of exactly one stick. How many non-congruent triangles can be formed with the sticks? - Vertex of the rectangle
Determine the coordinates of the vertex of the rectangle inscribed in the circle x²+y² -2x-4y-20=0 if you know that one of its sides lies on the line p: x+2y=0 - Calculate
Calculate the height of a tree that casts a shadow 22 m long if you know that at the same time, a pillar 2 m high casts a shadow 3 meters long. - Trapezoid 83
Trapezoid ABCD is composed of five triangles. Points E and G divide segment AB in the ratio 2:4:3 (in this order) into three segments. Point F is the midpoint of segment AD. Triangle AEF is isosceles and right-angled. Triangles GBC and CDG are right-angle - Quadrilateral ABCD
Construct a quadrilateral ABCD if AB = 10 cm, AD = 6 cm, DC = 6.5 cm and angle BCD = 90 degrees. - Quadrilateral in circle
A quadrilateral is inscribed in the circle. Its vertices divide the circle in a ratio of 1:2:3:4. Find the sizes of its interior angles. - Heptagon triangle probability
We randomly select three different points from the vertices of a regular heptagon and connect them with line segments. The probability that the resulting triangle will be isosceles is equal to: (A) 1/3 (B) 2/5 (C) 3/5 (D) 4/7 - Telephone calls
The random variable modelling the time between 2 phone calls has an exponential distribution with density f(x) = 10e^(−10x), x > 0. Calculate its distribution function and the probability that the time between calls does not exceed 5 seconds, the time - Polygon 3 Polygon ABCD is dilated, rotated, and translated to form polygon QWER. The endpoints A and B are at (0, -7) and (8, 8), and the endpoints QW are at (6, -6) and (2, 1.5). What is the scale factor of the dilation?
- Tournament match calculation
The long-term volleyball tournament is played one-on-one. So far, 11 teams have entered the competition. How many matches will be lost when two teams unsubscribe? - Exterior angles
In triangle ABC, the size of the exterior angle at vertex C is equal to 126°. The size of the internal angles at vertices A and B are in the ratio 5: 9. Calculate the size of the internal angles α, β, γ of triangle ABC. - Field map scale
The map shows a square-shaped field with a side length of 0.7 cm. Its area is 49 ha. Find the scale of the map. - Tennis ball parabola
In a tennis match, Adrien is 5 m from the net when he hits a ball 80 cm off the ground. The maximum height of its parabolic path passing through the net was 1.5 m. If the length of the court is 23.77 m, will the ball land inside the court? - 3 positive charges
Three equal positive charges Q are located at the vertices of an isosceles right triangle ABC. The right angle is at vertex A. The length of side AB is 1 m. What is the electric field strength at the center S of side BC, i.e., what force would act on a po - Linden shadow height
The length of the linden shadow is 429 cm. The length of the shadow meter is 78 cm. Calculate the height of the linden. - Observatories A,B
The target C is observed from two artillery observatories, A and B, 296 m apart. At the same time, angle BAC = 52°42" and angle ABC = 44°56". Calculate the distance of the target C from observatory A. - Triangle construction progress
An isosceles triangle ABY has a base AB of length 5 cm and an angle at the primary vertex of 50°. Write down the construction progress.
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