Similarity of triangles + triangle - practice problems - page 3 of 8
Number of problems found: 141
- Inclined plane
The body stays on an inclined plane and exerts a compressive force of 70N on it. Find the angle between the inclined plane and the horizontal if a gravitational force of 100N acts on the body. - Chimney and tree
Calculate the height of the factory chimney, which casts a shadow of 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long. - 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 triangles
The triangles ABC and A'B'C 'are similar, with a similarity coefficient of 2. The angles of the triangle ABC are alpha = 35° and beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '. - 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 - Triangle 28611
The land has a triangle shape with sides of 300m, 200m, and 245m. Draw it on a scale of 1:5 000. - Equilateral cone
We pour so much water into a container with the shape of an equilateral cone, the base of which has a radius r = 6 cm, that one-third of the volume of the cone is filled. How high will the water reach if we turn the cone upside down? - Right-angled 27683
Right-angled triangle XYZ is similar to triangle ABC, which has a right angle at the vertex X. The following applies a = 9 cm, x=4 cm, x =v-4 (v = height of triangle ABC). Calculate the missing side lengths of both triangles. - Similar triangles
In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D'E'F' is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D'E'F' if the similarity coefficient is one-seventh. - Similarity coefficient
In the triangle TMA, the length of the sides is t = 5cm, m = 3.5cm, and a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, and 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other. - Meneal's 26771
Show (using Meneal's theorem) that the center of gravity divides the line in a 1:2 ratio. - An observer
An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower? - Similarity 26441
How long a shadow casts a building 15 m high if the shadow of a meter rod is 90 cm? Sketch - similarity. - Cutting cone
A cone with a base radius of 10 cm and a height of 12 cm is given. At what height above the base should we divide it by a section parallel to the base so that the volumes of the two resulting bodies are the same? Express the result in cm. - Approximately 25381
The observer sees the tops of two trees at the same angle a. It is 9 m from one tree and 21 m from the other. The trees stand on a level. How tall is the second tree if the height of the first is 6 m? Remember that the eyes of a standing person are approx - 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. - The triangles
Two similar triangles, KLM and ABC, are given. Calculate the lengths of the remaining sides of the triangle KLM. If the lengths of the sides are a = 7 b = 5.6 c = 4.9 k = 5 - Lookout tower
Calculate the height of a lookout tower forming a shadow of 36 m if a column 2.5 m high has a shadow of 1.5 m at the same time. - Similarity of two triangles
The KLM triangle has a side length of k = 6.3cm, l = 8.1cm, m = 11.1cm. The triangle XYZ has a side length of x = 8.4cm, y = 10.8cm, z = 14.8cm. Are triangle KLM and XYZ similar? (write 0. If not, if yes, find and write the coefficient of a similarity) - Conical bottle
When a conical bottle rests on its flat base, the water in the bottle is 8 cm from its vertex. When the same conical bottle is turned upside down, the water level is 2 cm from its base. What is the height of the bottle?
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