# Similarity of triangles - practice problems - last page

#### Number of problems found: 152

- Cosine

Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and the hypotenuse 8.544. - See harmonics

Is it true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. The central segment crosses the intersection of the diagonals and is parallel to the bases. - 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. - Hexagon

There is a regular hexagon ABCDEF. If the area of the triangle ABC is 10, what is the area of the hexagon ABCDEF? I do not know how to solve it simply....

- 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. - 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? - Railways

Railways climb 2.8 ‰. Calculate the height difference between two points on the railway distant 5997 meters. - Reverse Pythagorean theorem

Given are the lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 66 dm, 60 dm, 23 dm ... Δ DEF: 20 mm, 15 mm, 25 mm ... Δ GHI: 16 cm, 20 cm, 12 cm ... Δ JKL: 58 cm, 63 cm, 23 cm ... Δ MNO: 115 mm, - Similarity

Are two right triangles similar if the first one has an acute angle 60° and the second one has an acute angle 30°?

- Climb

The road sign which informs the climb is 10.3%—the car drive 10 km along this road. What is the height difference that the car went? - Cone

The circular cone of height 15 cm and volume 5699 cm³ is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut. - Climb

The road has climbing 1:28. How big is an angle correspond to this climbing?

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