Similarity of triangles - high school - practice problems - page 2 of 3
Number of problems found: 60
- Secret treasure
Scouts have a tent in the shape of a regular quadrilateral pyramid with a side of the base of 4 m and a height of 3 m. Find the container's radius r (and height h) so that they can hide the largest possible treasure. - Right circular cone
The volume of a right circular cone is 5 liters. The cone is divided by a plane parallel to the base, one-third down from the vertex to the base. Calculate the volume of these two parts of the cone. - 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 s - Mast shadow
The mast has a 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at an angle of 15°. Determine the height of the mast if the sun above the horizon is at an angle of 33°. Use the law of sines.
- Isosceles 7661
The area of the isosceles triangle is 8 cm2, and its arm's length is 4 cm. Calculate the sizes of its interior angles. - 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 the trapezium area in cm square and calculate how many different perimeters - Calculate 7214
Two tangents are drawn from point C to a circle with a radius of 76 mm. The distance between the two contact points is 14 mm. Calculate the distance of point C from the center of the circle. - 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 point C, and point M lies on one-third of the side of the AC side closer to point A. Find what part of the ABC triangle contains the triangl - 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 an area of 10 cm². Find the area of the or
- Isosceles 6673
Isosceles triangle X'Y'Z' . It is similar to triangle XYZ. The base of triangle XYZ has length |XY|=4cm. The size of the angle at the X vertex is 45 degrees. Draw a triangle X'Y'Z' whose base is 8 cm long. - Intersection 6653
Two straight paths cross, making an angle alpha = 53 degrees 30'. There are two pillars on one of them, one at the intersection, the other at a distance of 500m from it. How far does one have to go from the intersection along the other road to see both po - MO Z9–I–2 - 2017
VO is a longer base in the VODY trapezoid, and the diagonal intersection K divides the VD line in a 3:2 ratio. The area of the KOV triangle is 13.5 cm². 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. Both laths cross 70 cm above the garage floor. How wide is the garage? - Calculate 5148
At a distance of 10 m from the river bank, they measured the base AB = 50 m parallel to the bank. Point C on the other bank of the river is visible from point A at an angle of 32°30' and from point B at an angle of 42°15'. Calculate the width of the river
- Hexagon cut pyramid
Calculate the volume of a regular 6-sided cut pyramid if the bottom edge is 30 cm, the top edge is 12 cm, and the side edge length is 41 cm. - V-belt
Calculate the length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm (distance between pulley axes) - 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 - Two similar triangles
Find unknown sides of a similar triangles: a = 6cm, b = 8cm, c =?, a '=?, b '= 12cm, c' = 15cm - Angle in RT
Determine the size of the smallest internal angle of a right triangle whose sides constitute the sizes of consecutive members of arithmetic progressions.
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