Reason + triangle - practice problems - last page
Number of problems found: 117
- Triangle ABC
Triangle ABC has side lengths m-1, m-2, and m-3. What has to be m to be a triangle a) rectangular b) acute-angled? - Right triangles
How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget the triangle inequality). - Carpet
The room is 10 x 5 meters. You have the role of carpet width of 1 meter. Make a rectangular cut of a roll. That piece of carpet will be the longest possible and will fit into the room. How long is a piece of carpet? Note: The carpet will not be parallel w - The fence
I'm building a cloth (board) fence. The boards are rounded in a semicircle at the top. The tops of the boards between the columns should copy an imaginary circle. The tip of the first and last board forms the chord of a circle whose radius is unknown. The
- Obtuse angle
Line OH is the height of the triangle DOM, and line MN is the bisector of angle DMO. the Obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image) - Combi-triangle
Each square side is marked 10 different points outside the square's vertices. How many triangles can be constructed from this set of points, where each vertex of the triangle lies on the other side of the square? - Train
The train is running at speeds of 96 km/h. From the beginning of braking to full stop, the train runs for 3.3 minutes. If the train slows the braking equally, calculate the distance from the location where you need to start to brake. - Hexagon
There is a regular hexagon ABCDEF. If the area of the triangle ABC is 22, what is the area of the hexagon ABCDEF? I do not know how to solve it simply.... - It is rectangular?
The size of two of the angles in a triangle is α=110°, β=40°. Is it a right triangle?
- River
From the observatory 11 m high and 24 m from the riverbank, river width appears in the visual angle φ = 13°. Calculate the width of the river. - Garden
The square garden area is 2/9 of triangle garden with sides 160 m, 100 m, and 100 m. How many meters of fencing need to fence a square garden? - Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Right
Determine angles of the right triangle with the hypotenuse c and legs a, b, if: 3a +4b = 4.9c - Mast
Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 13.3°. Determine the height of the mast if the sun above the horizon is at an angle 45°12'.
- Circles
Three circles of radius 30 cm, 28 cm, and 37 cm are mutually tangent. What is the triangle perimeter whose vertices are the circles' centers? - Chickens and rabbits
In the yard were chickens and rabbits. Together they had 23 heads and 76 legs. How many chickens and how many rabbits were in the yard? - N-gon angles
What is the sum of interior angles 8-gon? What is the internal angle of a regular convex 8-polygon?
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