Similarity of triangles - math problems
Number of problems found: 87
Calculate the cosine of the smallest internal angle in a right-angled triangle with cathetus 3 and 8 and with the hypotenuse 8.544.
- The straight
The straight path rises by 72 cm every 3 m of its length. How many meters will it climb to 350 m?
ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus.
Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
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 weight?
- Sides ratio
Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
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?
There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
How far from Peter stands 2m hight John? Petr is looking to John over ruler that keeps at arm's distant 60 cm from the eye and on the ruler John measured the height of 15 mm.
- Shadow and light
Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
- Tree shadow
The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
- See harmonics
It is true that the size of the central segment of any trapezoid is the harmonic mean size of its bases? Prove it. Central segment crosses the intersection of the diagonals and is parallel to the bases.
- 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?
Calculate a 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)
- The chimney
The chimney casts a shadow 45 meters long. The one-meter-long rod standing perpendicular to the ground has a shadow 90 cm long. Calculate the height of the chimney.
- 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.
- Divide an isosceles triangle
How to divide an isosceles triangle into two parts with equal contents perpendicular to the axis of symmetry (into a trapezoid and a triangle)?
On the road sign, which informs the climb is 8.7%. The car drive 5 km along this road. What is the height difference that the car went to?
- Reverse Pythagorean theorem
Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ... Δ DEF: 55 dm, 82 dm, 61 dm ... Δ GHI: 24 mm, 25 mm, 7 mm ... Δ JKL: 32 dm, 51 dm, 82 dm ... Δ MNO: 51 dm, 45 dm,
- Tree shadow
Tree perpendicular to the horizontal surface has a shadow 8.32 meters long. At the same time meter rod perpendicular to the horizontal surface has shadow 64 cm long. How tall is tree?
See also our trigonometric triangle calculator.