# Similarity of triangles + triangle - math problems

#### Number of problems found: 77

- A cliff

A line from the top of a cliff to the ground passes just over the top of a pole 5 ft high and meets the ground at a point 8 ft from the base of the pole. If the point is 93 ft from the base of the cliff, how high is the cliff? - Vertical rod

The vertical one meter long rod casts a shadow 150 cm long. Calculate the height of a column whose shadow is 36 m long at the same time. - Poplar shadow

The nine-meter poplar casts a shadow 16.2 m long. How long does a shadow cast by Peter at the same time, if it is 1.4 m high? - Chimney and tree

Calculate the height of the factory chimney, which casts a shadow 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°, beta = 48°. Determine the magnitudes of all angles of triangle A'B'C '. - 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, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other. - 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. - The triangles

The triangles KLM and ABC are given, which are similar to each other. 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 at the same time a column 2.5 m high has a shadow of 1.5 m. - 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 it 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? - Sides of right angled triangle

One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Secret treasure

Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base 4 m and a height of 3 m. Determine the radius r (and height h) of the container so that they can hide the largest possible treasure. - Two chords

Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle. - Lighthouse

Marcel (point J) lies in the grass and sees the top of the tent (point T) and behind it the top of the lighthouse (P). | TT '| = 1.2m, | PP '| = 36m, | JT '| = 5m. Marcel lies 15 meters away from the sea (M). Calculate the lighthouse distance from the sea - Trapezium diagonals

It is given trapezium ABCD with bases | AB | = 12 cm, |CD| = 8 cm. Point S is the intersection of the diagonals for which |AS| is 6 cm long. Calculate the length of the full diagonal AC. - Diagonals at right angle

In the trapezoid ABCD this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD? - Mast shadow

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. Use the law of sines.

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