Triangle + similarity of triangles - practice problems - page 4 of 8
Number of problems found: 141
- Similarity of triangles
If triangle ABC ~ to triangle XYZ, AC = 24, AB = 15, BC = 17, and XY = 9, what is the perimeter of triangle XYZ? Round all sides to 1 decimal place. - Similarity
Are two right triangles similar if the first one has an acute angle 70° and the second one has an acute angle 20°? - 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 '. - Two angles
The triangles ABC and A'B'C 'are similar. In the ABC triangle, the two angles are 25° and 65°. Explain why in the triangle A'B'C 'is the sum of two angles of 90 degrees.
- Two similar triangles
Find unknown sides of a similar triangles: a = 6cm, b = 8cm, c =?, a '=?, b '= 12cm, c' = 15cm - Similarity coefficient
The triangles ABC and A'B'C' are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A'B'C'. - Catheti
One of the catheti of the right triangle has a length of 12 cm. At what distance from the center of the hypotenuse is another cathetus? - Sun rays
If the sun's rays are at an angle of 60°, then the famous Great Pyramid of Egypt (which is now 137.3 meters high) has a 79.3 m long shadow. Calculate the current height of the neighboring Chephren pyramid, whose shadow is measured at the same time at 78.8 - 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.
- 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. - Reverse Pythagorean theorem
Given are the lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ... Δ DEF: 55 dm, 82 dm, 61 dm ... Δ GHI: 24 mm, 25 mm, 7 mm ... Δ JKL: 32 dm, 51 dm, 82 dm ... Δ MNO: 51 dm, 45 - Right-angled 80745
The area of a right-angled triangle KLM with a right angle at the vertex L is 60 mm square, and its hypotenuse k is 10 mm long. Triangles KLM and RST are similar. The similarity ratio is k=2.5. Calculate the area of triangle RST. - 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? - Geodesist
Triangle-shaped field (triangle ABC) has a side AB = 129 m. path XY is parallel to the side AB, which divides triangle ABC into two parts with the same area. What will be the length of path XY? Help, please, geodesist.
- The truncated
The truncated rotating cone has bases with radii r1 = 8 cm, r2 = 4 cm and height v = 5 cm. What is the volume of the cone from which the truncated cone originated? - 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? - Sides ratio
Calculate the circumference of a triangle with area 84 cm² if a:b:c = 10:17:21 - Similarity coefficient
The similarity ratio of two equilateral triangles is 4.3 (i.e., 43:10). The length of the side of the smaller triangle is 7.5 cm. Calculate the perimeter and area of the larger triangle. - Railways
Railways climb 2.8 ‰. Calculate the height difference between two points on the railway distant 5997 meters.
Do you have homework that you need help solving? Ask a question, and we will try to solve it.