# Similarity of triangles - math word problems

- 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. - Right circular cone

The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base. - 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. - Rectangular trapezoid

The ABCD rectangular trapezoid with the AB and CD bases is divided by the diagonal AC into two equilateral rectangular triangles. The length of the diagonal AC is 62cm. Calculate trapezium area in cm square and calculate how many differs perimeters of the - Equilateral triangle ABC

In the equilateral triangle ABC, K is the center of the AB side, the L point lies on one-third of the BC side near the point C, and the point M lies in the one-third of the side of the AC side closer to the point A. Find what part of the ABC triangle cont - Pyramid cut

We cut the regular square pyramid with a parallel plane to the two parts (see figure). The volume of the smaller pyramid is 20% of the volume of the original one. The bottom of the base of the smaller pyramid has a content of 10 cm^{2}. Find the area of the - Shadow

A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house? - 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. - Area of iso-trap

Find the area of an isosceles trapezoid if the lengths of its bases are 16 cm and 30 cm, and the diagonals are perpendicular to each other. - A boy

A boy of height 1.7m is standing 30m away from flag staff on the same level ground . He observes that the angle of deviation of the top of flag staff is 30 degree. Calculate the height of flag staff. - Shadow of tree

Miro stands under a tree and watching its shadow and shadow of the tree. Miro is 180 cm tall and its shade is 1.5 m long. The shadow of the tree is three times as long as Miro's shadow. How tall is the tree in meters? - MO Z9–I–2 - 2017

In the VODY trapezoid, VO is a longer base and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm^{2}. Find the area of the entire trapezoid. - Garage

There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the gara - 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 distant 20 m.

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See also our trigonometric triangle calculator.