Similarity of triangles - practice problems - page 7 of 8
Number of problems found: 158
- 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 - Ruler
Peter is looking at John over a ruler that keeps at an arm's distance of 60 cm from the eye, and on the ruler, John measured the height of 15 mm. John is 2 meters high. How far from Peter stands John? - Tree shadow
The tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time, a one-meter rod perpendicular to the horizontal surface has a shadow 64 cm long. How tall is the tree? - 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. - Lighthouse
The man, 180 cm tall, walks along the seafront directly to the lighthouse. The male shadow caused by the beacon light is initially 5.4 meters long. When the man approaches the lighthouse by 90 meters, its shadow is shorter by 3 meters. How tall is the lig - Sides ratio
Calculate the circumference of a triangle with an area of 84 cm² if a:b:c = 10:17:21
- Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent to the second leg b, is 5cm. - Two-meter 3473
A tree with an unknown height casts a shadow 18 m long at a time, while a two-meter pole casts a shadow of 2.4 m. How tall is the tree? - Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high does he fly? - 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? - Isosceles trapezoid
In an isosceles trapezoid KLMN, the intersection of the diagonals is marked by the letter S. Calculate the area of the trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm². - Shadow and light
Nine meters height poplar tree has a shadow 16.2 meters long. How long does shadow have at the same time as Joe if he is 1,4m tall? - Triangle KLB
It is given an equilateral triangle ABC. From point L, the midpoint of the side BC of the triangle, it is drawn perpendicular to the side AB. The intersection of the perpendicular and the side AB is point K. How many percent of the area of the triangle AB - Similar triangles The triangles ABC and XYZ are similar. Find the unknown lengths of the sides of the triangles. The lengths: a = 5cm, b = 8cm and x = 7.5cm z = 9cm.
- Area and two angles
Calculate the size of all sides and internal angles of a triangle ABC if it is given by area S = 501.9; and two interior angles α = 15°28' and β = 45°. - Rhombus
ABCD is a rhombus, ABD is an equilateral triangle, and AC is equal to 4. Find the area of the rhombus. - Diagonal in rectangle
In the ABCD rectangle is the center of BC, point E, and point F is the center of the CD. Prove that the lines AE and AF divide diagonal BD into three equal parts. - Similarity of squares
The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than an area of a square ABCD with side a: ... - Trapezoid IV
In a trapezoid ABCD (AB||CD) is |AB| = 15cm |CD| = 7 cm, |AC| = 12 cm, AC is perpendicular to BC. What area has a trapezoid ABCD?
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