Planimetrics + right triangle - practice problems - page 26 of 57
Number of problems found: 1136
- Transmitter 34201
A television transmitter 108 m high is anchored at 2/3 of its height (from the ground) by three ropes of equal length. How many meters of rope are needed for anchoring if it is embedded at a distance of 54 m from the foot of the mast, and we count 10% of - Glass mosaic
How many dm² glasses are necessary to produce 97 slides of a regular 6-gon, whose side has a length 21 cm? Assume that cutting glass waste is 10%. - River
Calculate how many permille river Dunaj average falls, if on section long 957 km flowing water from 1454 m AMSL to 101 m AMSL. - Trapezoid RT
The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length of 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio of 3:2. Calculate con - Consumption 17823
The roof has the shape of a regular hexagonal pyramid shell with a wall height of v = 5 m and a base edge of a = 4 m. Calculate the consumption of sheet metal to cover the roof, assuming 15% losses. - 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. - Center of gravity
In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity is T, find the area of the triangle ABT. - Climb in percentage
The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance between places A and B is 7.4 km. - Isosceles 5575
The picture shows an isosceles triangle VLK with a center of gravity of T. The base VL measures 16 cm, and the line KK1 measures 18 cm. How long is the VV1 line? - Equilateral 4301
Triangle ABC is equilateral with a side length of 8 cm. Points D, E, and F are the sides AB, BC, and AC midpoints. Calculate the area of triangle DEF. In what ratio is the area of triangle ABC to the area of triangle DEF? - Angles
In the triangle ABC, the ratio of angles is α:β = 4:5. The angle γ is 36°. How big are the angles α and β? - Circles
In the circle with a radius, 7.5 cm is constructed of two parallel chords whose lengths are 9 cm and 12 cm. Calculate the distance of these chords (if there are two possible solutions, write both). - Mirror
How far must Paul place a mirror to see the top of the tower 12 m high? The height of Paul's eyes above the horizontal plane is 160 cm, and Paul is from the tower distance of 20 m. - 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 - Cable car
Find the elevation difference of the cable car when it rises by 67 per mille, and the rope length is 930 m. - 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). - Gimli Glider
Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintains optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes for a plane to hit the ground from engine failure. - Obtuse angle
Line OH is the height of the triangle DOM, and line MN is the bisector of angle DMO. the Obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image) - Luiza
Luiza delivers newspapers in her neighborhood. If you plot the points (-1, 1), (4, 1), (4, -2), and (-1, -2), you will create a representation of the route she takes in miles. How many miles does her route cover? - Kilometers 73344
How many meters will the track ascend if it is 200 kilometers long and the ascent is 7 per mille?
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